Allouche, Jean-Paul; Shallit, Jeffrey The ubiquitous Prouhet-Thue-Morse sequence. (English) Zbl 1005.11005 Ding, C. (ed.) et al., Sequences and their applications. Proceedings of the international conference, SETA ’98, Singapore, December 14-17, 1998. London: Springer. Springer Series in Discrete Mathematics and Theoretical Computer Science. 1-16 (1999). Summary: We discuss a well-known binary sequence called the Thue-Morse sequence, or the Prouhet-Thue-Morse sequence. This sequence was introduced by A. Thue in 1906 (see JFM 39.0283.01) and rediscovered by M. Morse [Recurrent geodesics on a surface of negative curvature, Trans. Am. Math. Soc. 22, 84–100 (1921; JFM 48.0786.06)]. 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.For the entire collection see [Zbl 0974.00035]. Cited in 2 ReviewsCited in 123 Documents MSC: 11B85 Automata sequences 68R15 Combinatorics on words Keywords:binary sequence; Thue-Morse sequence Citations:JFM 48.0786.06; JFM 39.0283.01 PDF BibTeX XML Cite \textit{J.-P. Allouche} and \textit{J. Shallit}, in: Sequences and their applications. Proceedings of the international conference, SETA '98, Singapore, December 14--17, 1998. London: Springer. 1--16 (1999; Zbl 1005.11005) OpenURL Online Encyclopedia of Integer Sequences: Consider the Morse-Thue sequence (A010060) as defining a binary constant and convert it to decimal. Numerators of the sequence 1, 1/2, (1/2)/(3/4), ((1/2)/(3/4))/((5/6)/(7/8)), ... .