Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.2

On a Class of Thue-Morse Type Sequences

Ricardo Astudillo
Department of Mathematics
University of Illinois
Urbana, IL 61801

Abstract: We consider a class of binary sequences that generalize the Thue-Morse sequence. In particular, we investigate the occurrences of palindromes in such sequences. We also introduce the notion of the first difference of a binary sequence and characterize first differences of our class of Thue-Morse type sequences. Finally, we define the concept of a "change sequence" of a given binary sequence, a sequence which encodes the positions at which a binary sequence changes values. We characterize the change sequences corresponding to our class of Thue-Morse type sequences.

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(Concerned with sequence A010060.)

Received September 6 2002; revised version received April 28 2003; December 2 2003. Published in Journal of Integer Sequences December 12 2003.

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