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A197911 Representable by A001045 (Jacobsthal sequence). Complement of A003158. 6
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 (list; graph; refs; listen; history; text; internal format)
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
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. A056832.
Sequence in context: A218784 A039066 A304800 * A298007 A026363 A124678
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Oct 19 2011
STATUS
approved

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Last modified April 14 16:59 EDT 2024. Contains 371666 sequences. (Running on oeis4.)