A197911 - OEIS

%I #23 Jan 10 2023 01:35:45

%S 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,

%T 33,35,36,37,38,40,41,43,44,46,47,48,49,51,52,54,55,57,58,59,60,62,63,

%U 64,65,67,68,69,70,72,73,75,76,78,79,80,81,83,84,85,86,88

%N Representable by A001045 (Jacobsthal sequence). Complement of A003158.

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

%C 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

%C Partial sums of A056832. - _Reinhard Zumkeller_, Jul 29 2014

%H Reinhard Zumkeller, <a href="/A197911/b197911.txt">Table of n, a(n) for n = 0..10000</a>

%H L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., <a href="http://www.fq.math.ca/Scanned/10-5/carlitz3-a.pdf">Representations for a special sequence</a>, Fib. Quart., 10 (1972), 499-518, 550 (see page 499).

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

%o (Haskell)

%o a197911 n = a197911_list !! n

%o a197911_list = scanl (+) 0 a056832_list

%o -- _Reinhard Zumkeller_, Jul 29 2014

%o (Python)

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

%Y Cf. A001045, A003158, A010060. A050292.

%Y Cf. A056832.

%K easy,nonn

%O 0,3

%A _Philippe Deléham_, Oct 19 2011