%I #11 Jul 12 2021 03:38:46
%S 11,21,32,33,38,39,78,83,91,95,104,111,115,140,141,146,147,161,164,
%T 204,205,206,219,222,227,230,242,245,299,310,320,321,326,327,340,344,
%U 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 Numbers k such that the continued fractions for sqrt(k) and sqrt(k+1) have the same period.
%C Numbers k such that A003285(k) = A003285(k+1).
%H Chai Wah Wu, <a href="/A288186/b288186.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PeriodicContinuedFraction.html">Periodic Continued Fraction</a>
%e 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 Cf. A003285, A013943, A031400, A097853.
%K nonn
%O 1,1
%A _Ilya Gutkovskiy_, Jun 06 2017