This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288186 #12 Feb 16 2025 08:33:47 %S A288186 11,21,32,33,38,39,78,83,91,95,104,111,115,140,141,146,147,161,164, %T A288186 204,205,206,219,222,227,230,242,245,299,310,320,321,326,327,340,344, %U A288186 371,383,395,404,413,428,434,438,443,447,451,452,464,471,498,504,515,539,545,572,573,578,579,594,596,644,654,659,695 %N A288186 Numbers k such that the continued fractions for sqrt(k) and sqrt(k+1) have the same period. %C A288186 Numbers k such that A003285(k) = A003285(k+1). %H A288186 Chai Wah Wu, <a href="/A288186/b288186.txt">Table of n, a(n) for n = 1..10000</a> %H A288186 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PeriodicContinuedFraction.html">Periodic Continued Fraction</a> %e A288186 11 is in the sequence because sqrt(11) = 3 + 1/(3 + 1/(6 + 1/(3 + 1/(6 + 1/...)))), period 2: [3, 6] and sqrt(12) = 3 + 1/(2 + 1/(6 + 1/(2 + 1/(6 + 1/...)))), period 2: [2, 6]. %Y A288186 Cf. A003285, A013943, A031400, A097853. %K A288186 nonn %O A288186 1,1 %A A288186 _Ilya Gutkovskiy_, Jun 06 2017