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%I #14 Jul 06 2024 15:55:23
%S 258,262,278,302,322,579,597,633,651,654,669,681,687,717,726,1028,
%T 1052,1060,1068,1076,1084,1108,1116,1124,1132,1148,1164,1172,1212,
%U 1228,1244,1252,1268,1276,1292,1605,1630,1645,1655,1670,1795,1805,1830,1895,1905
%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 16.
%t cf16Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1}, ContinuedFraction[ s][[2]]];len=Length[cf];EvenQ[len] && cf[[len/2]] == 16]; Select[Range[2000],cf16Q] (* _Harvey P. Dale_, Mar 04 2018 *)
%K nonn
%O 1,1
%A _David W. Wilson_