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%I #12 Aug 18 2021 00:10:32
%S 72949,120490,121882,122581,179897,252173,337786,340114,341281,433253,
%T 435889,438533,663037,792629,796193,797978,801554,927994,933781,
%U 935714,943466,945409,947354,949301,1086493,1107433,1250765,1255241
%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 77.
%t cf77Q[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]] == 77]; Select[Range[1255300],cf77Q] (* _Harvey P. Dale_, Mar 30 2019 *)
%K nonn
%O 1,1
%A _David W. Wilson_
%E Corrected by _Harvey P. Dale_, Mar 30 2019