Some new Formulas for the Kolakoski Sequence A000002

Abdallah Hammam^1,

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

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

Abstract

We present here two formulas for the Kolakoski sequence (K_n)_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 n^th term of the sequence, K_n, according to K₁,K₂,...K_p, with improving so, the former known value given by Bordellès [2].

Keywords:
Kolakoski sequence recursion recursive formula.

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