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%I #16 Mar 24 2022 13:36:37
%S 5186,5198,5218,5282,5286,5294,5298,5302,5314,5318,5326,5342,5346,
%T 5366,5374,5378,5398,5414,5422,5438,5442,5462,5474,11667,11721,11733,
%U 11757,11769,11793,11811,11814,11829,11841,11892,11901,11964,11973,11991,12009
%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 72.
%t cf72Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1},ContinuedFraction[ s][[2]]];len=Length[cf];EvenQ[len]&&cf[[len/2]] == 72]; Select[Range[12100],cf72Q] (* _Harvey P. Dale_, Mar 24 2022 *)
%K nonn
%O 1,1
%A _David W. Wilson_
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