A072729 Denominator of rationals >= 1 whose continued fractions consist only of 1's and 2's, in ascending order by the sum of the continued fraction terms and descending by lowest order continued fraction terms to highest.

1, 1, 2, 2, 3, 3, 5, 5, 5, 5, 8, 7, 8, 8, 7, 8, 12, 13, 11, 12, 13, 12, 13, 11, 12, 13, 19, 19, 21, 17, 18, 19, 19, 21, 19, 19, 21, 17, 18, 19, 19, 21, 29, 31, 30, 31, 34, 27, 26, 29, 29, 31, 30, 31, 34

Offset

0,3

Links

Table of n, a(n) for n=0..54.

Formula

a(F(n)+F(n-3)+m) = a(F(n-1)+m) + a(F(n-3)+m) when 0<m<=F(n-2), n>2; a(F(n)+m) = 2*a(F(n-2)+m) + a(F(n-4)+m) when 0<m<=F(n-3), n>3; where a(0)=1, a(F(n+1)-1) = F(n) = n-th Fibonacci number; a(F(2n+1)) = n-th Pell number.

Crossrefs

Cf. A072728, A071585, A071766, A072726, A072727, A000129.

Sequence in context: A167755 A259788 A033302 * A057872 A059974 A045767

Adjacent sequences: A072726 A072727 A072728 * A072730 A072731 A072732

Keyword

easy,frac,nice,nonn

Author

Paul D. Hanna, Jul 09 2002

Status

approved