Geodesic
Some remarks on differentiable sequences and recursivity
Journal of integer sequences, Tome 13 (2010) no. 3.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $u$.
Classification : 68R15, 11Y55, 11B83
Keywords: kolakoski sequence, integer sequences, differentiable sequences, smooth sequences, combinatorics of words 
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     author = {F\'edou, Jean-Marc and Fici, Gabriele},
     title = {Some remarks on differentiable sequences and recursivity},
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Fédou, Jean-Marc; Fici, Gabriele. Some remarks on differentiable sequences and recursivity. Journal of integer sequences, Tome 13 (2010) no. 3. http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a7/