cp's OEIS Frontend

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.

A013647 Numbers k such that the period of the continued fraction for sqrt(k) contains no 1's.

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%I A013647 #15 Aug 09 2025 04:57:51
%S A013647 2,5,6,10,11,12,17,18,20,26,27,28,30,37,38,39,40,41,42,50,51,55,56,65,
%T A013647 66,68,72,82,83,84,87,89,90,101,102,104,105,110,122,123,126,128,130,
%U A013647 131,132,145,146,147,148,150,152,155,156,170,171,174,177,180,182,197,198,200,203
%N A013647 Numbers k such that the period of the continued fraction for sqrt(k) contains no 1's.
%D A013647 Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).
%H A013647 Amiram Eldar, <a href="/A013647/b013647.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%t A013647 cf1Q[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],False,FreeQ[ ContinuedFraction[ s][[2]],1]]]; Select[Range[250],cf1Q] (* _Harvey P. Dale_, Jun 06 2021 *)
%K A013647 nonn
%O A013647 1,1
%A A013647 _Clark Kimberling_