%I #18 Aug 18 2021 00:10:32
%S 11689,23458,37717,38890,56765,78569,79693,106501,138673,139418,
%T 171757,204745,210205,212041,248533,252533,255554,290069,291146,
%U 293306,294389,295474,296561,298741,299834,300929,302026,395225,402797,405337
%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 43.
%t cf43Q[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]] == 43]; Select[Range[406000],cf43Q] (* _Harvey P. Dale_, Aug 25 2019 *)
%K nonn
%O 1,1
%A _David W. Wilson_
%E First term 1850 removed by _Georg Fischer_, Jun 16 2019