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 A031550 that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 52. 1

%I #12 Aug 17 2021 23:48:27

%S 2706,2722,2734,2774,2786,2798,2802,2818,2838,2846,2854,2866,2878,

%T 2882,2894,2902,2914,6087,6117,6126,6132,6159,6189,6213,6231,6249,

%U 6261,6276,6297,6321,6333,6357,6369,6393,6411,6414,6429,6513,6537,6549,6558,10820

%N that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 52.

%H Harvey P. Dale, <a href="/A031550/b031550.txt">Table of n, a(n) for n = 1..1000</a>

%t cfQ[n_]:=Module[{sqr=Sqrt[n],c},If[IntegerQ[sqr],c={1},c=ContinuedFraction[ sqr][[2]]];EvenQ[Length[c]]&&c[[Length[c]/2]]==52]; Select[Range[11000], cfQ] (* _Harvey P. Dale_, Nov 28 2012 *)

%K nonn

%O 1,1

%A _David W. Wilson_

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Last modified September 21 19:40 EDT 2023. Contains 365503 sequences. (Running on oeis4.)