The aim of our investigation is an attempt to answer two still unsolved questions about Kolakoski sequence (K_n)_n≥1: Is there an explicit expression of the n^th term K_n, 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 K_n according to K₁, K₂, …K_p where In the second part, we define three sequences satisfying the condition U_iV_i=W_i, and using the fact that (V_i) increases at least exponentially while (W_i) does not, we conclude that (U_i) should converge to zero. Our argument is inductive but so strong to insure the validity of the conjecture in concern with density of twos.

Kolakoski sequence, recursive formula, asymptotic density.