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 A013644 #35 Aug 21 2025 08:30:31
%S A013644 7,14,23,28,32,33,34,47,55,60,62,75,78,79,95,96,98,119,126,128,136,
%T A013644 138,140,141,142,155,167,174,176,180,189,192,194,215,219,220,222,223,
%U A013644 248,252,254,266,287,299,300,305,312,315,318,320,321,322,335,359,368,377,390,392
%N A013644 Numbers k such that the continued fraction for sqrt(k) has period 4.
%D A013644 Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).
%H A013644 Amiram Eldar, <a href="/A013644/b013644.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A013644 Austin Mack and Timothy Sawicki, <a href="http://www.ncurproceedings.org/ojs/index.php/NCUR2012/article/viewFile/195/142">Pell's Equations Through Dynamical Systems</a>, 2012. [Broken link?]
%F A013644 See Austin Mack and Timothy Sawicki(2012).
%e A013644 The continued fraction for sqrt(7) is [2;1,1,1,4,...] with period 4, so 7 is in the sequence. The continued fractions sqrt(3) = [1;1,2,...] with period 2 and sqrt(13) = [3;1,1,1,1,6,...] with period 5 do not have period 4, so 3 and 13 are not in the sequence. - _Michael B. Porter_, Sep 20 2016
%t A013644 cfp4Q[n_]:=Module[{sr=Sqrt[n]},!IntegerQ[sr]&&Length[ ContinuedFraction[ sr][[2]]]==4]; Select[Range[500],cfp4Q] (* _Harvey P. Dale_, Jul 29 2014 *)
%Y A013644 Cf. A003285.
%K A013644 nonn
%O A013644 1,1
%A A013644 _Clark Kimberling_