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Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 73.
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%I #14 Aug 18 2021 00:10:32

%S 12109,66098,109642,110305,163337,306034,387173,388418,390914,393418,

%T 394673,481997,484777,596425,709493,719633,723029,841514,845186,

%U 850709,852554,854401,1124441,1137197,1145741,1298282,1300561,1457938,1460353,1489489

%N Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 73.

%t cf73Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1,1}, ContinuedFraction[ s][[2]]];len=Length[cf];OddQ[len] && cf[[(len+1)/2]]==73]; Select[Range[15*10^5],cf73Q] (* _Harvey P. Dale_, Oct 10 2017 *)

%K nonn

%O 1,1

%A _David W. Wilson_

%E Corrected and extended and definition clarified by _Harvey P. Dale_, Oct 10 2017