A074288 -id:A074288 - cp's OEIS frontend

A054353 Partial sums of Kolakoski sequence A000002.

1, 3, 5, 6, 7, 9, 10, 12, 14, 15, 17, 19, 20, 21, 23, 24, 25, 27, 29, 30, 32, 33, 34, 36, 37, 39, 41, 42, 43, 45, 46, 47, 49, 50, 52, 54, 55, 57, 59, 60, 61, 63, 64, 66, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 82, 84, 86, 87, 88, 90, 91, 93, 95, 96, 98, 100

Offset: 1

N. J. A. Sloane, May 07 2000

Alternate definition: n such that A000002(n) is different from A000002(n+1). - Nathaniel Johnston, May 02 2011

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
O. Bordelles and B. Cloitre, Bounds for the Kolakoski Sequence, J. Integer Sequences, 14 (2011), #11.2.1.
Bertran Steinsky, A Recursive Formula for the Kolakoski Sequence A000002, J. Integer Sequences, Vol. 9 (2006), Article 06.3.7.

Cf. A000002, A074272, A074286, A074288, A078649, A156077.

Cf. A088568 (partial sums of [3 - 2*A000002(n)]).

a054353 n = a054353_list !! (n-1)
a054353_list = scanl1 (+) a000002_list
-- Reinhard Zumkeller, Aug 03 2013

a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1+Mod[n-1, 2]}], {n, 3, 50}, {a2[[n]] } ]; Accumulate[a2] (* Jean-François Alcover, Jun 18 2013 *)

from itertools import accumulate
def alst(nn):
  K = Kolakoski() # using Kolakoski() in A000002
  return list(accumulate(next(K) for i in range(1, nn+1)))
print(alst(66))   # Michael S. Branicky, Jan 12 2021

A000002(a(n)) = (3+(-1)^n)/2; A000002(a(n)+1)=(3-(-1)^n)/2. - Benoit Cloitre, Oct 16 2005

a(n) = n + A074286(n) = 2*n - A156077(n) = A156077(n) + 2*A074286(n). - Jean-Christophe Hervé, Oct 05 2014

A074289 Values of A000002(n)*A054353(n) that are repeated.

Original entry on oeis.org

6, 10, 24, 34, 46, 64, 72, 82, 114, 118, 132, 142, 186, 196, 200, 222, 240, 268, 290, 298, 302, 316, 326, 344, 358, 370, 414, 436, 454, 460, 496, 518, 524, 600, 622, 640, 650, 658, 672, 696, 720, 750, 764, 782, 792, 846, 864, 878, 886, 890, 896, 914, 918

Offset: 1

Jon Perry, Sep 21 2002

Values that appear in A074288 multiple times.

			The Kolakoski sequence begins 1,2,2,1,1,2,1,... and its sequence of partial sums begins 1,3,5,6,7,9,10,... Multiplying the sequences term-by-term gives 1,6,10,6,7,18,10,... Since 6 and 10 appear more than once, they are both in this sequence.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A054353, A074288.

Extended and edited by Nathaniel Johnston, May 02 2011

cp's OEIS Frontend

A054353 Partial sums of Kolakoski sequence A000002.

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