A020440 Numbers k such that the period of the continued fraction for sqrt(k) contains exactly four 1's.

13, 21, 31, 57, 61, 67, 73, 74, 92, 106, 108, 109, 111, 112, 116, 129, 137, 158, 161, 162, 183, 185, 193, 204, 207, 236, 237, 243, 246, 251, 261, 262, 265, 273, 274, 275, 282, 297, 298, 308, 314, 317, 329, 332, 341, 346, 351, 355, 364, 375, 381, 383, 384, 388, 406, 412

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

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

Programs

Mathematica

Select[ Range@ 1900, !IntegerQ[ Sqrt@ #] && Count[ ContinuedFraction[ Sqrt@ #][[2]], 1] == 4 &] (* Robert G. Wilson v, Jul 03 2011 *)