A031511 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 13.

171, 179, 187, 191, 199, 211, 223, 680, 704, 768, 800, 808, 832, 864, 872, 896, 1527, 1587, 1671, 1815, 1875, 1959, 2019, 2712, 2776, 2824, 3032, 3208, 3288, 3352, 3464, 3544, 3592, 4235, 4315, 4415, 4435, 4535, 4615, 4735, 4815, 4835, 4915, 5035, 5135

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Mathematica

ct13Q[n_]:=Module[{s=Sqrt[n], cf}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[ s][[2]]]; EvenQ[Length[cf]]&&cf[[(Length[cf])/2]] == 13]; Select[Range[5200], ct13Q] (* Harvey P. Dale, Sep 04 2018 *)

Crossrefs

Sequence in context: A187140 A185845 A045149 * A101273 A136365 A031900

Adjacent sequences: A031508 A031509 A031510 * A031512 A031513 A031514

Keyword

nonn

Author

David W. Wilson

Extensions

Definition edited by Harvey P. Dale, Jul 16 2022

Status

approved