A013649 Numbers k such that the period of the continued fraction for sqrt(k) contains exactly two 1's.

14, 19, 22, 23, 29, 33, 34, 45, 47, 52, 53, 54, 59, 60, 62, 69, 70, 71, 77, 78, 79, 85, 95, 96, 98, 107, 114, 117, 118, 119, 125, 127, 138, 140, 141, 142, 149, 153, 154, 164, 165, 167, 173, 178, 187, 188, 189, 192, 194, 202, 205, 206, 216, 218, 219, 220, 221, 222, 223, 229

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 (terms 1..8300 from Robert Israel)

Maple

filter:= n -> not issqr(n) and numboccur(1, numtheory:-cfrac(sqrt(n), periodic, quotients)[2])=2:
select(filter, [$1..500]); # Robert Israel, Nov 01 2018

Mathematica

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

Crossrefs

Sequence in context: A165228 A205866 A248134 * A013657 A013653 A360169

Adjacent sequences: A013646 A013647 A013648 * A013650 A013651 A013652

Keyword

nonn

Author

Clark Kimberling

Status

approved