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 A020640 #27 Dec 31 2024 06:45:57
%S A020640 1,2,4,5,6,8,10,12,16,18,20,22,26,34,37,40,42,44,48,52,54,60,62,64,70,
%T A020640 76,79,88,94,96,102,104,108,114,118,122,130,136,152,156,158,170,172,
%U A020640 174,194,196,202,207,210,217,228,234,238,239,248,262,268,280,281
%N A020640 Successive record periods of continued fraction for sqrt(k) (period of continued fraction for sqrt(A013645(n+1))).
%H A020640 Patrick McKinley, <a href="/A020640/b020640.txt">Table of n, a(n) for n=1..512</a>
%F A020640 a(n) = A003285(A013645(n+1)). - _Pontus von Brömssen_, Nov 24 2024
%t A020640 per[n_] := ContinuedFraction[Sqrt[n]][[2]] // Length; record = 0; t = Reap[For[n = 1, n < 2*10^4, n++, If[ !IntegerQ[Sqrt[n]], p = per[n]; If[p > record, record = p; Print[{n, p}]; Sow[{n, p}]]]]][[2, 1]]; A020640 = t[[All, 2]] (* _Jean-François Alcover_, Dec 27 2012 *)
%t A020640 DeleteDuplicates[Table[If[IntegerQ[Sqrt[n]],Nothing,Length[ContinuedFraction[Sqrt[n]][[2]]]],{n,20000}],GreaterEqual] (* _Harvey P. Dale_, Dec 28 2023 *)
%Y A020640 Cf. A003285, A013645.
%K A020640 nonn,nice
%O A020640 1,2
%A A020640 _David W. Wilson_