A Cogent Argument that Supports the Conjecture of Keane in Kolakoski Sequence A000002

The aim of our investigation is an attempt to answer two still unsolved questions about Kolakoski sequence (Kn)n≥1: Is there an explicit expression of the nth term Kn, and the second one, known as the conjecture of Keane, claims that the asymptotic density of twos, is In the first section of this paper, we present a new formula for Kn according to K1, K2, …Kp where In the second part, we define three sequences satisfying the condition UiVi=Wi, and using the fact that (Vi) increases at least exponentially while (Wi) does not, we conclude that (Ui) should converge to zero. Our argument is inductive but so strong to insure the validity of the conjecture in concern with density of twos