A031687 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 99.

198997, 200785, 201682, 298237, 420073, 556741, 561226, 710938, 719393, 891497, 895277, 899065, 1086205, 1094557, 1098745, 1300129, 1311554, 1316138, 1533269, 1543189, 1545674, 1548161, 1553141, 1558129, 1560626, 1817833, 2062937

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Mathematica

ct99Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1, 1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; OddQ[len] && cf[[Floor[ len/2]]] == cf[[Ceiling[len/2]]]==99]; Select[Range[2063000], ct99Q] (* Harvey P. Dale, Oct 09 2021 *)

Crossrefs

Sequence in context: A290780 A255782 A205638 * A234034 A154531 A043592

Adjacent sequences: A031684 A031685 A031686 * A031688 A031689 A031690

Keyword

nonn

Author

David W. Wilson

Extensions

First term 9802 removed by Georg Fischer, Jun 16 2019

Status

approved