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On the rational approximation to the Thue–Morse–Mahler numbers

Yann Bugeaud (2011)

Annales de l’institut Fourier

Let ( t k ) k 0 be the Thue–Morse sequence on { 0 , 1 } defined by t 0 = 0 , t 2 k = t k and t 2 k + 1 = 1 - t k for k 0 . Let b 2 be an integer. We establish that the irrationality exponent of the Thue–Morse–Mahler number k 0 t k b - k is equal to 2 .

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