A013650 Numbers k such that the period of the continued fraction for sqrt(k) contains exactly three 1's.

7, 32, 75, 88, 136, 215, 279, 280, 312, 403, 427, 560, 711, 736, 851, 880, 923, 1007, 1067, 1272, 1311, 1363, 1431, 1495, 1736, 1855, 1887, 1955, 1976, 1995, 2128, 2159, 2184, 2272, 2511, 2567, 2640, 2728, 2880, 3055, 3211, 3560, 3751, 3811, 3927, 3984

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

References

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

Links

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

Programs

Mathematica

Select[ Range@ 1900, !IntegerQ[ Sqrt@ #] && Count[ ContinuedFraction[ Sqrt@ #][[2]], 1] == 3 &] (* Robert G. Wilson v, Jul 03 2011 *)