A013651 Numbers k such that the period of the continued fraction for sqrt(k) contains at least two 1's.

7, 13, 14, 19, 21, 22, 23, 29, 31, 32, 33, 34, 43, 44, 45, 46, 47, 52, 53, 54, 57, 58, 59, 60, 61, 62, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 85, 86, 88, 91, 92, 93, 94, 95, 96, 97, 98

Offset

1,1

References

Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

q[k_] := Module[{c = ContinuedFraction[Sqrt[k]]}, Length[c] == 2 && Count[c[[2]], 1] >= 2]; Select[Range[100], q] (* Amiram Eldar, Aug 09 2025 *)

Crossrefs

Sequence in context: A353443 A332480 A233593 * A379301 A050931 A072864

Adjacent sequences: A013648 A013649 A013650 * A013652 A013653 A013654

Keyword

nonn

Author

Clark Kimberling

Status

approved