Squares and overlaps in the Thue-Morse sequence and some variants
Shandy Brown, Narad Rampersad, Jeffrey O. Shallit, Troy Vasiga · RAIRO - Theoretical Informatics and Applications · 2006
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.