A031668 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 80.

40829, 132577, 195485, 197257, 362629, 365041, 466778, 473633, 584057, 587117, 590185, 850613, 852458, 1002626, 1006634, 1014674, 1016689, 1018706, 1024769, 1184473, 1188829, 1351085, 1360397, 1365065, 1374425, 1541042, 1548497

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Subsequence of A003814.

Programs

Mathematica

cf80Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{0,0},ContinuedFraction[s][[2]]];len=Length[cf];OddQ[len]&&cf[[Floor[len/2]]]==cf[[Ceiling[len/2]]]==80]; Select[Range[155*10^4],cf80Q] (* Harvey P. Dale, Jul 24 2022 *)

Extensions

First term 6401 removed by Georg Fischer, Jun 16 2019