A197911 Representable by A001045 (Jacobsthal sequence). Complement of A003158.

0, 1, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 32, 33, 35, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 75, 76, 78, 79, 80, 81, 83, 84, 85, 86, 88

Offset: 0

Author

Philippe Deléham, Oct 19 2011

Keywords

• easy
• nonn

Comments

a(n) modulo 2 is the Prouhet-Thue-Morse sequence A010060.

The sequence of Jacobsthal numbers A001045 begins [1, 1, 3, 5, 11, 21, ...] with two occurrences of the term 1. Allowing for this, we find that the numbers representable as a sum of distinct Jacobsthal numbers form A050292. - Peter Bala, Feb 02 2013

Partial sums of A056832. - Reinhard Zumkeller, Jul 29 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Representations for a special sequence, Fib. Quart., 10 (1972), 499-518, 550 (see page 499).

Crossrefs

Cf. A001045, A003158, A010060. A050292.

Cf. A056832.

Programs

Haskell

a197911 n = a197911_list !! n
a197911_list = scanl (+) 0 a056832_list
-- Reinhard Zumkeller, Jul 29 2014

Python

def A197911(n): return n+sum((~(i+1)&i).bit_length()&1 for i in range(n)) # Chai Wah Wu, Jan 09 2023

Formula

a(n) = Sum_{k>=0} A030308(n,k)*A001045(k+2).