A031601 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 13.

409, 1181, 2258, 3562, 3802, 3925, 5305, 5897, 8269, 9829, 10834, 11041, 12389, 15737, 16745, 17785, 21757, 23029, 23633, 24554, 25178, 26869, 27194, 27521, 28181, 28514, 28849, 30554, 30901, 32413, 33853, 36073, 36185, 40841, 41362, 41765, 42170

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..150

Crossrefs

Subsequence of A003814.

Programs

Mathematica

cf13Q[n_]:=Module[{per=ContinuedFraction[Sqrt[n]][[2]]},OddQ[Length[ per]]&&per[[Floor[Length[per]/2]+1]]==13]; nn=43000;With[{terms = Complement[Range[nn], Range[Floor[Sqrt[nn]]]^2]}, Select[terms, cf13Q]] (* Harvey P. Dale, Nov 23 2011 *)

Extensions

Corrected by Harvey P. Dale, Nov 23 2011