A225186 Squares in the Thue-Morse word A001285.

11, 22, 1212, 2121, 121121, 212212, 12211221, 21122112, 122112122112, 211221211221, 1221211212212112, 2112122121121221, 122121121221122121121221, 211212212112211212212112, 12212112211212211221211221121221, 21121221122121122112122112212112

Offset: 1

Author

N. J. A. Sloane, May 04 2013

Keywords

• nonn

Comments

A square in an infinite word w is a factor of the form uu, where u has finite length.

Consists of 11, 22, 121121, 212212 and their repeated images under the morphism 1 -> 12, 2 -> 21.

Replacing {1,2} by {0,1} gives the squares in A010060.

Links

• James D. Currie and Narad Rampersad, Infinite words containing squares at every position, arXiv:0803.1189 [math.CO], 2008; or also, RAIRO-Theor. Inf. Appl. 44, 113-124 (2010).

Crossrefs

Cf. A001285, A020060, A225188 (square roots).