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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 76.
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%I #15 Jul 06 2024 16:09:53

%S 5778,5794,5806,5822,5826,5854,5862,5874,5878,5926,5938,5942,5958,

%T 5998,6018,6022,6038,6046,6062,6082,12999,13017,13044,13071,13089,

%U 13143,13173,13182,13188,13251,13254,13269,13287,13323,13326,13341,13353,13377,13389

%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 76.

%t cf76Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s][[2]]];len=Length[cf];EvenQ[len]&&cf[[len/2]]== 76]; Select[ Range[14000],cf76Q] (* _Harvey P. Dale_, Aug 27 2019 *)

%K nonn

%O 1,1

%A _David W. Wilson_