A031666 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 78.

13933, 123985, 124690, 126106, 185021, 258233, 260269, 262313, 347146, 550925, 553897, 559865, 679417, 823178, 953201, 957109, 959066, 962986, 964949, 966914, 972821, 974794, 1120093, 1286797, 1295885, 1467482, 1474757, 1477186

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Subsequence of A003814.

Programs

Mathematica

cf78Q[n_]:=Module[{s=Sqrt[n],len,cf},cf=If[IntegerQ[s],{1,1},ContinuedFraction[s][[2]]];len= Length[ cf];OddQ[len]&&cf[[Floor[len/2]]]==cf[[Ceiling[len/2]]]==78]; Select[Range[ 1480000],cf78Q] (* Harvey P. Dale, Dec 16 2023 *)

Extensions

First term 6085 removed by Georg Fischer, Jun 16 2019