A013652 Numbers k such that the period of the continued fraction for sqrt(k) contains at least three 1's.

7, 13, 21, 31, 32, 43, 44, 46, 57, 58, 61, 67, 73, 74, 75, 76, 86, 88, 91, 92, 93, 94, 97, 103, 106, 108, 109, 111, 112, 113, 115, 116, 124, 129, 133, 134, 135, 136, 137, 139, 151, 157, 158, 159, 160, 161, 162, 163, 166, 172, 179, 181, 183, 184, 185, 186, 190, 191, 193, 199

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] >= 3]; Select[Range[100], q] (* Amiram Eldar, Aug 09 2025 *)

Crossrefs

Sequence in context: A135275 A304005 A304947 * A099988 A076947 A138077

Adjacent sequences: A013649 A013650 A013651 * A013653 A013654 A013655

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from David W. Wilson

Status

approved