A031603 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 15.

2858, 3074, 5122, 7177, 7517, 9773, 10169, 13681, 14149, 16673, 17189, 17713, 17978, 18514, 20525, 21097, 22265, 22861, 26041, 27337, 27997, 30113, 32213, 33653, 35594, 35969, 37489, 37874, 38261, 39041, 39434, 39829, 45673, 52825, 54785, 55717

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Subsequence of A003814.

Programs

Mathematica

opct15Q[n_]:=Module[{sr=Sqrt[n],cf,len},cf=If[IntegerQ[sr],{}, ContinuedFraction[ sr][[2]]];len=Length[cf];OddQ[len]&&Take[cf,{Floor[ len/2],Floor[len/2]+1}]=={15,15}]; Select[Range[56000],opct15Q] (* Harvey P. Dale, Jun 11 2013 *)

Extensions

Corrected by Harvey P. Dale, Jun 11 2013