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

0,4

Links

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

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]

Crossrefs

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

Sequence in context: A328790 A319773 A256188 * A292601 A301364 A309503

Adjacent sequences: A072724 A072725 A072726 * A072728 A072729 A072730

Keyword

easy,frac,nice,nonn

Author

Paul D. Hanna, Jul 09 2002

Status

approved