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

Author

Paul D. Hanna, Jul 09 2002

Keywords

• easy
• frac
• nice
• nonn

Crossrefs

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

Formula

a(F(n)+F(n-3)+m) = a(F(n-1)+m) + a(F(n-3)+m) when 02; a(F(n)+m) = 2*a(F(n-2)+m) + a(F(n-4)+m) when 03; where a(0)=1, a(F(n+1)-1) = F(n) = n-th Fibonacci number; a(F(2n+1)) = n-th Pell number.