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N. J. A. Sloane, The On-line Encyclopedia of Integer Sequences, published electronically at http://oeis.org.

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A Necessary Condition for the Existence of the Asymptotic Density in Kolakoski Sequence

1Département de Mathématiques, Faculté des sciences, Université Moulay Ismaïl, 50020 Meknès, Morocco


Turkish Journal of Analysis and Number Theory. 2018, Vol. 6 No. 2, 57-60
DOI: 10.12691/tjant-6-2-5
Copyright © 2018 Science and Education Publishing

Cite this paper:
Abdallah Hammam. A Necessary Condition for the Existence of the Asymptotic Density in Kolakoski Sequence. Turkish Journal of Analysis and Number Theory. 2018; 6(2):57-60. doi: 10.12691/tjant-6-2-5.

Correspondence to: Abdallah  Hammam, Département de Mathématiques, Faculté des sciences, Université Moulay Ismaïl, 50020 Meknès, Morocco. Email: a.hammam@fs.umi.ac.ma

Abstract

We investigate here the Oldenburger-Kolakoski sequence with K1=1. In the first part, we give some expressions of the discrepancy function δ(n) representing the difference between 2s and 1s in K1K2Kn. The discrepancy could be interpreted as a perturbation of a certain equilibrium. Our main result is a necessary and sufficient condition for the existence of the asymptotic density. In the last section, we present an algorithm to generate the sequence terms and a formula for the term Kn.

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