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 A031406 #16 Aug 18 2021 00:13:13
%S A031406 11,19,23,40,87,96,152,159,216,219,235,335,336,344,392,415,455,515,
%T A031406 535,567,592,615,688,707,747,816,848,875,888,920,927,944,976,1072,
%U A031406 1080,1099,1111,1143,1183,1199,1200,1211,1243,1320,1328,1359,1360,1456,1507,1547
%N A031406 Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 3.
%H A031406 T. D. Noe, <a href="/A031406/b031406.txt">Table of n, a(n) for n = 1..1000</a>
%t A031406 n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[EvenQ[len] && c[[2, len/2]] == 3, AppendTo[t, n]]]]; t (* _T. D. Noe_, Apr 04 2014 *)
%t A031406 cf3Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s][[2]]];len=Length[cf];EvenQ[len]&&cf[[len/2]] == 3]; Select[Range[1600],cf3Q] (* _Harvey P. Dale_, Aug 15 2015 *)
%Y A031406 Cf. A031404-A031423.
%K A031406 nonn
%O A031406 1,1
%A A031406 _David W. Wilson_