Problem 52283. Find numbers in the Popular Computing Z-sequence

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Here’s a quick one. In 1977 the magazine </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Popular Computing</w:t></w:r><w:r><w:t> sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"a1 = a2 = 1\"/></w:customXmlPr><w:r><w:t>a_1 = a_2 = 1</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"a_n = |2 a_{n-2} + a_{n-1} – n|\"/></w:customXmlPr><w:r><w:t>a_n = |2 a_{n-2} + a_{n-1} – n|</w:t></w:r></w:customXml><w:r><w:t> for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n &gt; 2\"/></w:customXmlPr><w:r><w:t>n &gt; 2</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Among the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to find the index of the first occurrence of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"k\"/></w:customXmlPr><w:r><w:t>k</w:t></w:r></w:customXml><w:r><w:t> (including the five numbers above) in the </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Popular Computing </w:t></w:r><w:r><w:t>Z-sequence. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 195.817px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.9083px; transform-origin: 407px 97.9083px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 130.958px 7.79167px; transform-origin: 130.958px 7.79167px; unicode-bidi: normal; "><span style="">Here’s a quick one. In 1977 the magazine </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.9167px 7.79167px; transform-origin: 59.9167px 7.79167px; unicode-bidi: normal; "><span style="font-style: italic; ">Popular Computing</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.533px 7.79167px; transform-origin: 192.533px 7.79167px; unicode-bidi: normal; "><span style=""> sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”</span></span></div><div style="block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="a1 = a2 = 1" style="width: 72.5px; height: 20px;" width="72.5" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; "><span style=""> and </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="a_n = |2 a_{n-2} + a_{n-1} – n|" style="width: 134.5px; height: 20px;" width="134.5" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.79167px; transform-origin: 12.05px 7.79167px; unicode-bidi: normal; "><span style=""> for </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="n > 2" style="width: 36.5px; height: 18px;" width="36.5" height="18"></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.65px 7.79167px; transform-origin: 383.65px 7.79167px; unicode-bidi: normal; "><span style="">Among the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.775px 7.79167px; transform-origin: 178.775px 7.79167px; unicode-bidi: normal; "><span style="">Write a function to find the index of the first occurrence of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">k</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.925px 7.79167px; transform-origin: 129.925px 7.79167px; unicode-bidi: normal; "><span style=""> (including the five numbers above) in the </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.8583px 7.79167px; transform-origin: 61.8583px 7.79167px; unicode-bidi: normal; "><span style="font-style: italic; ">Popular Computing </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8417px 7.79167px; transform-origin: 40.8417px 7.79167px; unicode-bidi: normal; "><span style="">Z-sequence. </span></span></div></div></div>

Solve

Solution Stats

22 Solutions
13 Solvers

Last Solution submitted on May 06, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers13

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 52283. Find numbers in the Popular Computing Z-sequence

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers13

Suggested Problems

More from this Author221

Problem Tags

Community Treasure Hunt

Problem 52283. Find numbers in the Popular Computing Z-sequence

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers13

Suggested Problems

More from this Author221

Problem Tags

Community Treasure Hunt

Players

WeChat