Geodesic
Some remarks on differentiable sequences and recursivity
Journal of integer sequences, Tome 13 (2010) no. 3
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 
@article{JIS_2010__13_3_a7,
     author = {F\'edou,  Jean-Marc and Fici,  Gabriele},
     title = {Some remarks on differentiable sequences and recursivity},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {3},
     zbl = {1184.68371},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a7/}
}
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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/