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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 69.
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%I #14 Feb 18 2024 12:18:18

%S 4763,4779,4783,4787,4799,4803,4811,4827,4831,4859,4871,4879,4883,

%T 4903,4919,4923,4931,4943,4947,4951,4967,4987,4991,4999,5003,5011,

%U 5023,5027,5039,19048,19072,19104,19112,19200,19296,19328,19456,19488,19496,19520

%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 69.

%t cf69Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s][[2]]];len= Length[ cf];EvenQ[len]&&cf[[len/2]]==69]; Select[Range[20000],cf69Q] (* _Harvey P. Dale_, Jul 06 2019 *)

%K nonn

%O 1,1

%A _David W. Wilson_