Journal of Integer Sequences, Vol. 13 (2010), Article 10.3.2

Some Remarks on Differentiable Sequences and Recursivity

Jean-Marc Fédou and Gabriele Fici
Laboratoire d'Informatique, Signaux et Systèmes de Sophia-Antipolis
UMR6070 - CNRS et Université de Nice-Sophia Antipolis
2000, route des Lucioles
06903 Sophia-Antipolis Cedex


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.

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(Concerned with sequences A000002 A078880 A156253 A156351 A156728.)

Received December 8 2009; revised versions received February 25 2010. Published in Journal of Integer Sequences, February 25 2010.

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