The ubiquitous Prouhet-Thue-Morse sequence

A Adler; A Cobham; A Restivo; A Rényi; B Mathan de; CE Arshon; CR Prouhet; D Robbins; DH Lehmer; DR Woods; E Artin; F Axel; F Axel; FM Dekking; G Christol; G Christol; GA Hedlund; H Fredricksen; J Berstel; J Berstel; J Berstel; J Shallit; J Tromp; J-i Tamura; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-P Allouche; J-Y Yao; JA Brzozowski; JB Roberts; JC Martin; JC Martin; L Carlitz; L Jonker; M Boffa; M Cosnard; M Dekking; M Euwe; M Keane; M Lothaire; M Morse; M Morse; M Morse; M Morse; M. Boffa and F. Point, Identités de Thue-Morse dans les groupes; O Salon; P Borwein; P Collet; P Flajolet; P Séébold; PS Novikov; R Nürnberg; S Dubuc; SI Adian; V Komornik; W Parry; WM Schmidt

Abstract

We discuss a well-known binary sequence called the ThueMorse sequence, or the Prouhet-Thue-Morse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences

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