Geodesic
Bounds for the Kolakoski sequence
Journal of integer sequences, Tome 14 (2011) no. 2
The Kolakoski sequence $(K_{n})$ is perhaps one of the most famous examples of self-describing sequences for which some problems are still open. In particular, one does not know yet whether the density of 1's in this sequence is equal to 1/2. This work, which does not answer this question, provides explicit bounds for the main sequences related to $(K_{n})$. The proofs rest on a new identity involving the partial sums of $(K_{n})$ and on Dirichlet's pigeonhole principle which allows us to improve notably on the error-term.
Classification : 11B37, 11B83, 11B85
Keywords: kolakoski sequence, Dirichlet's pigeonhole principle 
@article{JIS_2011__14_2_a0,
     author = {Bordell\`es,  Olivier and Cloitre,  Benoit},
     title = {Bounds for the {Kolakoski} sequence},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {2},
     zbl = {1230.11026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_2_a0/}
}
TY  - JOUR
AU  - Bordellès,  Olivier
AU  - Cloitre,  Benoit
TI  - Bounds for the Kolakoski sequence
JO  - Journal of integer sequences
PY  - 2011
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JIS_2011__14_2_a0/
LA  - en
ID  - JIS_2011__14_2_a0
ER  - 
%0 Journal Article
%A Bordellès,  Olivier
%A Cloitre,  Benoit
%T Bounds for the Kolakoski sequence
%J Journal of integer sequences
%D 2011
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/JIS_2011__14_2_a0/
%G en
%F JIS_2011__14_2_a0
Bordellès,  Olivier; Cloitre,  Benoit. Bounds for the Kolakoski sequence. Journal of integer sequences, Tome 14 (2011) no. 2. http://geodesic.mathdoc.fr/item/JIS_2011__14_2_a0/