A228803 Denominators of rational numbers having continued fraction consisting entirely of 1s and 2s.

1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 15, 17, 18, 19, 21, 24, 25, 26, 27, 29, 30, 31, 34, 37, 40, 41, 43, 44, 45, 46, 47, 49, 50, 55, 56, 58, 61, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 79, 80, 81, 89, 91, 93, 97, 98, 99, 100, 101, 104, 105, 106, 108

Offset

1,2

Comments

Related to Zaremba's conjecture. - Charles R Greathouse IV, Sep 12 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

Rationals given by continued fractions as lexicographically ordered tuples of 1s and 2s: [1] = 1/1, [2] = 2/1, [1,1] = 2/1, [1,2] = 3/2, [2,1] = 3/1, [2,2] = 5/2, [1,1,1] = 3/2.  The list continues: 5/3, 4/3, 7/5, 5/2, 8/3, 7/3, 12/5, 5/3, 8/5, 7/4, 12/7, 7/5, 11/8, 10/7, 17/12, 8/3, 13/5, 11/4, 19/7, 12/5, 19/8, 17/7, 29/12.

Mathematica

Sort[Union[Denominator[Map[FromContinuedFraction, Flatten[Map[Tuples[{1, 2}, #] &, Range[13]], 1]]]]]

Crossrefs

Cf. A228804, A228805.

Sequence in context: A039082 A340608 A047503 * A037014 A261131 A225061

Adjacent sequences: A228800 A228801 A228802 * A228804 A228805 A228806

Keyword

nonn,easy

Author

Clark Kimberling, Sep 04 2013

Status

approved