

A228803


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


3



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
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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



