A031868 Numbers k such that the period of the continued fraction for sqrt(k) contains exactly 100 ones.

11806, 11839, 13729, 16246, 17461, 17761, 18061, 18529, 20409, 21241, 21718, 21871, 22171, 22177, 22549, 22699, 23929, 24151, 24369, 24829, 25078, 25429, 26116, 27529, 28102, 28603, 28807, 28813, 29383, 29449, 29476, 29649, 29661, 30669, 30796, 30961

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

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

Programs

Mathematica

q[k_] := Module[{c = ContinuedFraction[Sqrt[k]]}, Length[c] == 2 && Count[c[[2]], 1] == 100]; Select[Range[30000], q] (* Amiram Eldar, Aug 14 2025 *)