A072727 Denominator of the rationals >= 1 whose continued fractions consist of only even terms, in ascending order by the sum of the continued fraction terms and descending by lowest order continued fraction terms to highest.

0, 1, 1, 2, 1, 2, 4, 5, 1, 2, 4, 5, 6, 9, 9, 12, 1, 2, 4, 5, 6, 9, 9, 12, 8, 13, 17, 22, 13, 20, 22, 29, 1, 2, 4, 5, 6, 9, 9, 12, 8, 13, 17, 22, 13, 20, 22, 29, 10, 17, 25, 32, 25, 38, 40, 53, 17, 28, 38, 49, 32, 49, 53, 70

Offset: 0

Author

Paul D. Hanna, Jul 09 2002

Keywords

• easy
• frac
• nice
• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..1023

Crossrefs

Cf. A072726, A071585, A071766, A072728, A072729, A000129.

Formula

a(n) = A072726(m) where m = n - 2^(floor(log_2(n))). a(0) = 0, a(2^k) = 1, a(2^k + 1) = 2, a(2^k - 1) = the k-th Pell number. [Corrected by Sean A. Irvine, Oct 22 2024]