Adamczewski, Boris; Bugeaud, Yann A short proof of the transcendence of Thue-Morse continued fractions. (English) Zbl 1132.11330 Am. Math. Mon. 114, No. 6, 536-540 (2007). From the text: The Thue-Morse sequence \(t=(t_n)_{n\geq0}\) on the alphabet \(\{a,b\}\) is defined as follows: \(t_n=a\) (respectively, \(t_n=b\)) if the sum of the binary digits of \(n\) is even (respectively, odd). M. Queffélec [J. Number Theory 73, No. 2, 201–211 (1998; Zbl 0920.11045)] showed that the continued fraction is transcendental. The purpose of our note is to give a new, simpler proof of this theorem that illustrates the fruitful interplay between combinatorics on words and Diophantine approximation. Cited in 8 Documents MSC: 11J70 Continued fractions and generalizations 11J81 Transcendence (general theory) Citations:Zbl 0920.11045 PDFBibTeX XMLCite \textit{B. Adamczewski} and \textit{Y. Bugeaud}, Am. Math. Mon. 114, No. 6, 536--540 (2007; Zbl 1132.11330) Full Text: DOI Online Encyclopedia of Integer Sequences: Consider the Morse-Thue sequence (A010060) as defining a binary constant and convert it to decimal.