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 A206579 #9 Jul 12 2021 02:01:38
%S A206579 2,3,7,13,43,94,133,211,244,478,604,886,1279,1516,1726,3004,3271,3436,
%T A206579 4111,4846,4999,6484,6694,7606,9739,10399,10774,12919,13126,15031,
%U A206579 16699,17599,17614,18379,19231,25516,25939,32839,32971,39526,40639,42046,42571
%N A206579 Numbers k such that the periodic part of the continued fraction of sqrt(k) has more ones than any smaller k.
%C A206579 The number 1 is the most common number in continued fractions of sqrt(k) for k = 1, 2, 3, ....
%C A206579 Most of the terms in this sequence are the product of a prime and a power of 2. There are only three exceptions less than 10^6: 133, 253621, and 375181.
%e A206579 The periodic part of the continued fraction of sqrt(7) is (1, 1, 1, 4), which has more ones than any smaller square root.
%t A206579 t = {{2, 0}}; Do[If[! IntegerQ[Sqrt[k]], cnt = Count[ContinuedFraction[Sqrt[k]][[2]], 1]; If[cnt > t[[-1, 2]], AppendTo[t, {k, cnt}]]], {k, 3, 50000}]; Transpose[t][[1]]
%Y A206579 Cf. A206578 (least number having exactly n ones in its continued fraction).
%Y A206579 Cf. A206580 (number of ones for a(n)).
%K A206579 nonn
%O A206579 1,1
%A A206579 _T. D. Noe_, Feb 29 2012