%I #14 Feb 24 2023 10:48:22
%S 1851,1867,1871,1879,1899,1907,1923,1927,1931,1951,1979,1987,1999,
%T 2003,2011,2023,7400,7424,7488,7520,7528,7552,7584,7592,7624,7680,
%U 7712,7720,7776,7808,7872,7880,7904,7976,8000,8032,8096,16647,16707,16719,16791
%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 43.
%t cf43Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s][[2]]];len=Length[cf];EvenQ[len]&&cf[[len/2]] == 43]; Select[Range[17000],cf43Q] (* _Harvey P. Dale_, Jan 08 2019 *)
%K nonn
%O 1,1
%A _David W. Wilson_
%E Definition corrected by _Harvey P. Dale_, Feb 24 2023
