

A074286


Partial sum of the Kolakoski sequence (A000002) minus n.


8



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

a(n) is the number of 2's in the Kolakoski word of length n (see first formula below).  JeanChristophe Hervé, Oct 05 2014


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.


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).  JeanChristophe Hervé, Oct 05 2014


EXAMPLE

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 11=0, 32=1, 53=2, 64=2, 75=2, 96=3, ... .


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]] (* JeanFrançois Alcover, Jun 18 2013 *)


CROSSREFS

Cf. A000002 (Kolakoski sequence), A054353 (partial sums of K. sequence), A156077 (number of 1's in K. sequence).
Sequence in context: A073174 A107631 A029098 * A025769 A103563 A008625
Adjacent sequences: A074283 A074284 A074285 * A074287 A074288 A074289


KEYWORD

nonn,easy


AUTHOR

Jon Perry, Sep 21 2002


EXTENSIONS

Corrected offset from Nathaniel Johnston, May 02 2011


STATUS

approved



