{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":3011,"title":"Self-similarity 2 - Every third term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\r\n* seq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_third = [0, 1, 2, 1, 2]\r\n\r\nSince seq_every_third = seq_orig_first_third, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term Problem 3010\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\"\u003eProblem 3010\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_2(seq)\r\n\r\ntf = 0;\r\n\r\nend\r\n","test_suite":"%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 9, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 12, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 1, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 180, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 12, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 2, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 144, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 2, 1, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 8, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 3, 5, 2, 4, 6, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 3, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 6, 4, 2, 4, 12, 6, 4, 8, 0, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 6, 4, 0, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 3, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 20, 56, 32, 24, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 16, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 4, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 8, 4, 2, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 40, 56, 32, 64, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 111, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 4, 3, 4, 3, 1, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 2, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 5, 2, 4, 5, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 8, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 1, 4, 0, 2, 0, 0, 6, 4, 1, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 2, 6, 4, 2, 4, 12, 6, 4, 8, 2, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":66,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:22:00.000Z","updated_at":"2026-03-11T15:38:45.000Z","published_at":"2015-02-13T04:22:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3010\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3010,"title":"Self-similarity 1 - Every other term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\r\n* seq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\r\n\r\nSince seq_every_other = seq_orig_first_half, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\"\u003eProblem 3011\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_1(seq)\r\n\r\ntf = 0;\r\n\r\nend","test_suite":"%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 2, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 390, 390, 54, 630, 174, 366];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 4, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 8, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 11, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 144, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 312, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 4, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 16, 16, 8, 16, 16, 32, 8, 8, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 318, 390, 54, 630, 174, 366];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 3, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 5, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 5, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 18, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, -1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:04:32.000Z","updated_at":"2026-03-16T14:11:36.000Z","published_at":"2015-02-13T04:04:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_other = [0, , 1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3011\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3012,"title":"Self-similarity 3 - Every other pair of terms","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]\r\n* seq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]\r\n\r\nSince seq_every_other_pair = seq_orig_first_half, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term Problem 3010\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]\u003c/li\u003e\u003cli\u003eseq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_other_pair = seq_orig_first_half, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\"\u003eProblem 3010\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\"\u003eProblem 3011\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_3(seq)\r\n\r\ntf = 0;\r\n\r\nend\r\n","test_suite":"%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 3, 7, 15, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 1, 7, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 2, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 2, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 5, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 2, 5, 15, 5, 15, 15, 52, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 4, 2, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 7, 7, 15, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 3, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 2, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 5, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 2, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 2, 5, 15, 5, 15, 15, 52, 1, 2, 5, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 2, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 7, 7, 15, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 15, 7, 7, 15, 15, 31, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:36:07.000Z","updated_at":"2026-03-16T14:22:23.000Z","published_at":"2015-02-13T04:36:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_other_pair = seq_orig_first_half, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3010\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3011\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":3011,"title":"Self-similarity 2 - Every third term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\r\n* seq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_third = [0, 1, 2, 1, 2]\r\n\r\nSince seq_every_third = seq_orig_first_third, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term Problem 3010\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\"\u003eProblem 3010\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_2(seq)\r\n\r\ntf = 0;\r\n\r\nend\r\n","test_suite":"%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 9, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 12, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 1, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 180, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 12, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 4, 1, 2, 5, 4, 5, 8, 1, 2, 5, 2, 3, 6, 5, 6, 9, 4, 5, 8, 5, 6, 9, 8, 9, 12, 1, 2, 5, 2, 3, 6, 5, 6, 9, 2, 3, 6, 3, 4, 7, 6, 7, 10, 5, 6, 9, 6, 7, 10, 9, 10, 13, 4, 5, 8, 5, 6, 9, 8, 9, 12, 5, 6, 9, 6, 7];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 12, 36, 12, 84, 72, 36, 96, 180, 12, 216, 144, 84, 168, 288, 72, 372, 216, 36, 240, 504, 96, 432, 288, 180, 372, 504, 12, 672, 360, 216, 384, 756, 144, 648, 576, 84, 456, 720, 168, 1080, 504, 288, 528, 1008, 72, 864, 576, 372, 684, 1116, 216, 1176, 648, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 2, 1, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 7, 2, 5, 8, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 3, 5, 2, 4, 6, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 3, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 6, 4, 2, 4, 12, 6, 4, 8, 0, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 6, 4, 0, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 3, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 20, 56, 32, 24, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 4, 6, 3, 6, 9, 2, 4, 6, 4, 8, 16, 6, 12, 18, 3, 6, 9, 6, 12, 18, 9, 18, 27, 2, 4, 6, 4, 8, 12, 6, 12, 18, 4, 8, 12, 8, 16, 24, 12, 24, 36, 6, 12, 18, 12, 24, 36, 18, 36, 54, 3, 6, 9, 6, 12, 18, 9, 18, 27, 6, 12, 18, 12, 24, 36, 18, 36, 54, 9, 18, 27, 18, 36, 54, 27, 54];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 4, 5, 2, 5, 8, 1, 4, 5, 4, 13, 14, 5, 14, 17, 2, 5, 8, 5, 14, 17, 8, 17, 26, 1, 4, 5, 4, 13, 14, 5, 14, 17, 4, 13, 14, 13, 40, 41, 14, 41, 44, 5, 14, 17, 14, 41, 44, 17, 44, 53, 2, 5, 8, 5, 14, 17, 8, 17, 26, 5, 14, 17, 14, 41, 44, 17, 44, 53, 8, 17, 26, 17, 44, 53, 26, 53, 80];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 6, 8, 4, 2, 10, 12, 0, 4, 8, 4, 4, 0, 0, 14, 8, 2, 12, 12, 0, 4, 8, 0, 8, 0, 6, 4, 4, 6, 8, 24, 4, 16, 8, 0, 8, 0, 10, 18, 8, 12, 34, 12, 0, 24, 44, 4, 8, 24, 8, 28, 12, 4, 46, 48, 4, 28, 36, 0, 16];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 20, 24, 4, 32, 52, 4, 24, 48, 40, 56, 32, 64, 116, 72, 4, 80, 120, 32, 48, 96, 52, 124, 56, 4, 160, 120, 24, 128, 244, 48, 72, 192, 20, 152, 80, 56, 312, 168, 32, 176, 240, 24, 96, 192, 116, 228, 124, 72, 280, 216, 4, 288, 416, 80, 120, 240, 120, 248, 128, 32, 500];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 11, 12, 2, 12, 22, 1, 11, 12, 11, 111, 112, 12, 112, 122, 2, 12, 22, 12, 112, 122, 22, 122, 222, 1, 11, 12, 11, 111, 112, 12, 112, 122, 11, 111, 112, 111, 1111, 1112, 112, 1112, 1122, 12, 112, 122, 112, 1112, 1122, 122, 1122, 1222, 2, 12, 22, 12, 112];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 4, 3, 4, 3, 1, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 2, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 1, 2, 3, 2, 3, 1, 3, 1, 2, 1, 2, 3, 3, 1, 2, 1, 2, 3, 2, 3, 1, 1, 2, 3, 2, 3, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 5, 2, 4, 5, 3, 5, 7, 2, 4, 6, 3, 5, 7, 4, 6, 8, 1, 2, 3, 3, 4, 5, 5, 6, 7, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 2, 3, 4, 4, 5, 6, 6, 7, 8, 3, 4, 5, 5, 6, 7, 7, 8, 9, 4, 5, 6, 6, 7, 8, 8, 9, 10, 1, 3, 5, 2, 4, 6, 3, 5, 7, 3, 5, 7, 4, 6, 8, 5, 7, 9, 5, 7, 9];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3, 3, 6, 9, 6, 6, 3, 9, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 4, 4, 12, 4, 4, 8, 4, 12, 4, 4, 12, 4, 12, 4, 12, 4, 4, 12, 4, 4, 4, 4, 20, 12, 4, 4, 12, 12, 4, 4, 4, 12, 12, 4, 12, 4, 12, 12, 12, 4, 4, 4, 12, 4, 4, 4, 4, 20, 12, 12, 12, 4, 12, 4, 4, 12, 4, 12, 12, 4, 4, 4, 36, 4, 4, 12, 4, 12, 4, 4, 12, 12, 20, 4, 4, 12, 4, 12, 4, 12, 4, 4, 36];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [\t1, 2, 0, 2, 6, 0, 1, 4, 0, 2, 0, 0, 6, 4, 1, 0, 6, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 12, 0, 0, 4, 0, 0, 0, 0, 6, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 6, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 12, 0, 0, 4, 0, 2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 6, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 0, 2, 6, 0, 2, 6, 4, 2, 4, 12, 6, 4, 8, 2, 10, 0, 0, 16, 8, 6, 4, 12, 4, 14, 8, 2, 34, 12, 4, 16, 40, 12, 12, 48, 6, 28, 8, 4, 44, 24, 8, 16, 44, 0, 12, 24, 10, 58, 16, 0, 28, 36, 0, 24, 100, 16, 16, 48, 8, 28, 16, 6, 62];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 2, 1, 2, 3, 2, 3, 0, 1, 2, 3, 2, 3, 0, 3, 0, 1, 2, 3, 0, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_2(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":66,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:22:00.000Z","updated_at":"2026-03-11T15:38:45.000Z","published_at":"2015-02-13T04:22:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every third term. The problem set assumes that you start with the first element and then take every third element thereafter of the original sequence, and compare that result to the first third of the original sequence. The function should return true if the extracted sequence is equal to the first third of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_third = [0, , , 1, , , 2, , , 1, , , 2, , ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_third = [0, 1, 2, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_third = seq_orig_first_third, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3010\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3010,"title":"Self-similarity 1 - Every other term","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\r\n* seq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\r\n\r\nSince seq_every_other = seq_orig_first_half, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/li\u003e\u003cli\u003eseq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\"\u003eProblem 3011\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\"\u003eProblem 3012\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_1(seq)\r\n\r\ntf = 0;\r\n\r\nend","test_suite":"%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 2, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 390, 390, 54, 630, 174, 366];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 4, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 8, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 11, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 144, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 1, 3, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 3, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 3, 3, 0, 0, 2, 1, 4, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 4, 0, 1, 2, 0, 3, 0, 4, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 3, 2, 3, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 4, 4, 0, 4, 8, 0, 0, 4, 4, 8, 0, 0, 8, 0, 0, 4, 8, 4, 0, 8, 0, 0, 0, 0, 12, 8, 0, 0, 8, 0, 0, 4, 0, 8, 0, 4, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 4, 12, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 4, 16, 0, 0, 8, 0, 0, 0, 4, 8, 8, 0, 0, 0, 0, 0, 8, 4, 8, 0, 0, 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 8, 4, 0, 12, 8];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 24, 24, 96, 24, 144, 96, 192, 24, 312, 144, 288, 96, 336, 192, 576, 24, 432, 312, 480, 144, 768, 288, 576, 96, 744, 336, 960, 192, 720, 576, 768, 24, 1152, 432, 1152, 312, 912, 480, 1344, 312, 1008, 768, 1056, 288, 1872, 576, 1152, 96, 1368, 744, 1728, 336];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 4, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 16, 16, 8, 16, 16, 32, 8, 8, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 6, 6, 30, 6, 30, 30, 54, 6, 102, 30, 78, 30, 78, 54, 150, 6, 102, 102, 126, 30, 270, 78, 150, 30, 150, 78, 318, 54, 174, 150, 198, 6, 390, 102, 270, 102, 222, 126, 390, 30, 246, 270, 270, 78, 510, 150, 294, 30, 390, 150, 510, 78, 318, 318, 390, 54, 630, 174, 366];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 6, 5, 5, 4, 5, 3, 4, 3, 5, 4, 4, 3, 4, 3, 3, 2, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3, 6, 5, 5, 4, 5, 4, 4, 3, 5, 4, 4, 3, 4, 3, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 5, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 5, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 18, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, -1, -4, -3, 1, -2, 3, 1, -2, -1, 3, 2, -1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -1, 0, 1, 1, -2, -1, 1, 0, 1, 1, 0, 1, -5, -4, 1, -3, 4, 1, -3, -2, 5, 3, -2, 1, -3, -2, 1, -1, 4, 3, -1, 2, -3, -1, 2, 1, -3, -2, 1, -1, 2, 1, -1, 0, 1, 1, 0, 1, -1, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 7, 6, 11, 5, 14, 9, 13, 4, 15, 11, 18, 7, 17, 10, 13, 3, 14, 11, 19, 8, 21, 13, 18, 5, 17, 12, 19];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_1(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":72,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:04:32.000Z","updated_at":"2026-03-16T14:11:36.000Z","published_at":"2015-02-13T04:04:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_other = [0, , 1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_other = seq_orig_first_half, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3011\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3012\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3012,"title":"Self-similarity 3 - Every other pair of terms","description":"Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003chttps://oeis.org/selfsimilar.html OEIS page\u003e for more information.\r\n\r\nIn this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\r\n\r\nFor example,\r\n\r\n* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]\r\n* seq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series) \r\n* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]\r\n\r\nSince seq_every_other_pair = seq_orig_first_half, the set is self-similar.\r\n\r\nThis problem is related to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term Problem 3010\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011\u003e.","description_html":"\u003cp\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the \u003ca href = \"https://oeis.org/selfsimilar.html\"\u003eOEIS page\u003c/a\u003e for more information.\u003c/p\u003e\u003cp\u003eIn this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cul\u003e\u003cli\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]\u003c/li\u003e\u003cli\u003eseq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series)\u003c/li\u003e\u003cli\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince seq_every_other_pair = seq_orig_first_half, the set is self-similar.\u003c/p\u003e\u003cp\u003eThis problem is related to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\"\u003eProblem 3010\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\"\u003eProblem 3011\u003c/a\u003e.\u003c/p\u003e","function_template":"function [tf] = self_similarity_3(seq)\r\n\r\ntf = 0;\r\n\r\nend\r\n","test_suite":"%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 3, 7, 15, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 1, 7, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 2, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 2, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 5, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 2, 5, 15, 5, 15, 15, 52, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 4, 2, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 7, 7, 15, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 3, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 2, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 5, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 2, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 2, 5, 15, 5, 15, 15, 52, 1, 2, 5, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 4, 2, 4, 4, 8, 2, 2, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4];\r\ntf_corr = 1;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n\r\n%%\r\nseq = [0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 7, 7, 15, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 15, 7, 7, 15, 15, 31, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31];\r\ntf_corr = 0;\r\nassert(isequal(self_similarity_3(seq),tf_corr))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-13T04:36:07.000Z","updated_at":"2026-03-16T14:22:23.000Z","published_at":"2015-02-13T04:36:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSelf-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/selfsimilar.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOEIS page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eseq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince seq_every_other_pair = seq_orig_first_half, the set is self-similar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3010\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 3011\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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