Geodesic
Bounds for the Kolakoski sequence
Journal of integer sequences, Tome 14 (2011) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Bordell\`es, Olivier and Cloitre, Benoit},
     title = {Bounds for the {Kolakoski} sequence},
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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/