Some Remarks on Differentiable Sequences and Recursivity

International audience; We investigate the recursive structure of differentiable sequences over the alphabet {1, 2}. We derive a recursive formula for the (n + 1)-th symbol of a differentiable sequence, which yields to a new recursive formula for the Kolakoski sequence. Finally, we show that the sequence of absolute differences of consecutive symbols of a differentiable sequence u is a morphic image of the run-length encoding of u.