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Article

Some new Formulas for the Kolakoski Sequence A000002

1Département de Mathématiques et Informatique, Université Moulay Ismaїl Faculté des sciences, Meknès, Morocco


Turkish Journal of Analysis and Number Theory. 2016, Vol. 4 No. 3, 54-59
DOI: 10.12691/tjant-4-3-1
Copyright © 2016 Science and Education Publishing

Cite this paper:
Abdallah Hammam. Some new Formulas for the Kolakoski Sequence A000002. Turkish Journal of Analysis and Number Theory. 2016; 4(3):54-59. doi: 10.12691/tjant-4-3-1.

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

Abstract

We present here two formulas for the Kolakoski sequence (Kn)n≥1. The first one is in concern with the frequency of the letters 1 and 2 in this sequence. Our investigation seems to support the hypothesis of the Keane’s conjecture. In the second part of this paper, we give an expression of the nth term of the sequence, Kn, according to K1,K2,...Kp, with improving so, the former known value given by Bordellès [2].

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