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Some Remarks on Differentiable Sequences and Recursivity
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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

France

**Abstract:**

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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