Problem 51580. Construct a continued fraction for a square root

Numbers can be expressed as continued fractions of the form
x = a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/...)))
Some continued fractions—such as those for e and π--continue forever without a discernable pattern in the coefficients, while the coefficients of continued fractions for square roots eventually repeat. For example,
sqrt(2) = 1+(1/(2+1/(2+1/(2+1/...))))
sqrt(14) = 3+1/(1+1/(2+1/(1+1/(6+1/...))))
Write a function that takes a non-square integer and returns the values of until the values repeat.
This problem celebrates my finally cracking Cody Problem 1215 by James. If you struggle with Test 8, as I did, remember that MATLAB cannot represent decimals with infinite precision.

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17.39% Correct | 82.61% Incorrect
Last Solution submitted on Jul 14, 2024

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