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%I #14 Nov 05 2023 05:05:59
%S 8283,8287,8291,8311,8331,8351,8363,8371,8387,8403,8419,8423,8431,
%T 8443,8447,8459,8467,8483,8519,8523,8527,8531,8539,8543,8551,8563,
%U 8599,8623,8627,8647,33128,33160,33184,33256,33280,33408,33416,33448,33472,33504
%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 91.
%t cf91Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s]][[2]];len=Length[cf];EvenQ[len]&&cf[[len/2]]==91]; Select[Range[34000],cf91Q]//Quiet (* _Harvey P. Dale_, Feb 01 2019 *)
%K nonn
%O 1,1
%A _David W. Wilson_