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

0,3

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).

Formula

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

Prog

(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

Crossrefs

Cf. A001045, A003158, A010060. A050292.

Cf. A056832.

Sequence in context: A218784 A039066 A304800 * A298007 A026363 A124678

Adjacent sequences: A197908 A197909 A197910 * A197912 A197913 A197914

Keyword

easy,nonn,changed

Author

Philippe Deléham, Oct 19 2011

Status

approved