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A031418 Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central terms both equal to 5. 1

%I

%S 73,373,449,565,610,757,1021,1145,1193,1594,1669,1906,2053,2074,2138,

%T 2314,2477,2593,2861,3065,3145,4129,4346,4373,4469,4498,4721,5018,

%U 5114,5386,5741,6025,6317,6617,6737,6925,7241,7489,7522,7897,7978,8017,8186,8314

%N Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central terms both equal to 5.

%H T. D. Noe, <a href="/A031418/b031418.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 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 Cf. A031404-A031423.

%K nonn

%O 1,1

%A _David W. Wilson_

%E Corrected and extended by _Harvey P. Dale_, Feb 22 2013

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Last modified September 28 01:20 EDT 2020. Contains 337388 sequences. (Running on oeis4.)