A074286 Partial sum of the Kolakoski sequence (A000002) minus n.
0, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11, 12, 12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 21, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 34, 35, 35
Offset: 1
Examples
The Kolakoski sequence is 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, ...; the partial sums are 1, 3, 5, 6, 7, 9, ..., so the sequence is 1-1=0, 3-2=1, 5-3=2, 6-4=2, 7-5=2, 9-6=3, ... .
Links
- 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.
Crossrefs
Programs
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Mathematica
a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1 + Mod[n - 1, 2]}], {n, 3, 50}, {a2[[n]]}]; a3 = Accumulate[a2]; a3 - Range[Length[a3]] (* Jean-François Alcover, Jun 18 2013 *)
Formula
a(n)=#{1<=k<=n : A000002(k)=2}. - Benoit Cloitre, Feb 03 2009
a(n) = A054353(n) - n. - Nathaniel Johnston, May 02 2011
a(n) = n - A156077(n). - Jean-Christophe Hervé, Oct 05 2014
Extensions
Corrected offset from Nathaniel Johnston, May 02 2011
Comments