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%I #14 Jul 06 2024 16:08:27
%S 4626,4642,4678,4694,4702,4722,4726,4742,4766,4786,4798,4802,4806,
%T 4818,4822,4834,4838,4846,4854,4866,4882,4894,4898,10407,10446,10452,
%U 10473,10479,10497,10524,10533,10551,10569,10581,10587,10596,10617,10623,10641
%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 68.
%t cf68Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s][[2]]];len=Length[cf];EvenQ[len]&&cf[[len/2]]==68]; Select[Range[11000],cf68Q] (* _Harvey P. Dale_, Jan 10 2019 *)
%K nonn
%O 1,1
%A _David W. Wilson_