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Numbers k such that the continued fraction for sqrt(k) has period 13.
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%I #12 Aug 07 2023 12:53:44

%S 193,281,481,565,593,746,778,997,1082,1138,1250,1514,1930,2042,2426,

%T 2477,2837,2930,3121,3145,3338,3413,3625,3797,3853,3925,4001,4058,

%U 4421,4745,5122,5234,5741,6010,6170,6481,7025,7250,7418,7730,7757,7877,7930,8450

%N Numbers k such that the continued fraction for sqrt(k) has period 13.

%t cf13Q[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],1,Length[ContinuedFraction[s][[2]]]==13]]; Select[ Range[9000],cf13Q] (* _Harvey P. Dale_, Aug 07 2023 *)

%K nonn

%O 1,1

%A _David W. Wilson_