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.

A031418 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 5.

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%I A031418 #26 Aug 18 2021 00:33:16
%S A031418 73,373,449,565,610,757,1021,1145,1193,1594,1669,1906,2053,2074,2138,
%T A031418 2314,2477,2593,2861,3065,3145,4129,4346,4373,4469,4498,4721,5018,
%U A031418 5114,5386,5741,6025,6317,6617,6737,6925,7241,7489,7522,7897,7978,8017,8186,8314
%N A031418 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 5.
%H A031418 T. D. Noe, <a href="/A031418/b031418.txt">Table of n, a(n) for n = 1..1000</a>
%e A031418 The simple continued fraction expansion of sqrt(73) = [8, 1, 1, 5, 5, 1, 1, 16, ...] of odd period 7 with a pair of central terms both equal to 5. Another example is sqrt(373) = [19, 3, 5, 5, 3, 38, ...] of odd period 5 with a pair of central terms both equal to 5. - _Michael Somos_, Apr 03 2014
%t A031418 opct5Q[n_]:=Module[{s=Sqrt[n],cf,len},If[IntegerQ[s],cf={1,1}, cf= ContinuedFraction[s][[2]]];len=Length[cf];OddQ[len] && cf[[Floor[len/2]]] == cf[[Ceiling[len/2]]]==5]; Select[Range[10000],opct5Q] (* _Harvey P. Dale_, Feb 22 2013 *)
%Y A031418 Cf. A031404-A031423.
%Y A031418 Subsequence of A003814.
%K A031418 nonn
%O A031418 1,1
%A A031418 _David W. Wilson_
%E A031418 Corrected and extended by _Harvey P. Dale_, Feb 22 2013