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Squares and overlaps in the Thue-Morse sequence and some variants
Shandy Brown, Narad Rampersad, Jeffrey Shallit, Troy Vasiga
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 40 / Issue 3 / July 2006

Published online by Cambridge University Press:

18 October 2006, pp. 473-484

Print publication:

July 2006
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We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are 2-regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of 2) contains an overlap.