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%I #14 Jul 06 2024 16:07:44
%S 4227,4231,4243,4247,4259,4271,4283,4299,4307,4319,4327,4339,4363,
%T 4391,4411,4419,4423,4443,4447,4451,4463,4467,4483,4487,16904,16928,
%U 16936,16992,17000,17024,17056,17088,17096,17120,17128,17152,17216,17224,17248
%N Numbers k such 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 65.
%t cf65Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s][[2]]];len=Length[cf];EvenQ[len]&&cf[[len/2]] == 65]; Select[Range[17300],cf65Q] (* _Harvey P. Dale_, Dec 29 2019 *)
%K nonn
%O 1,1
%A _David W. Wilson_