Journal of Integer Sequences, Vol. 16 (2013), Article 13.2.3

On Rational Approximation of the Binary Thue-Morse-Mahler Number


Yann Bugeaud
Mathématiques
Université de Strasbourg
7 rue René Descartes
67084 Strasbourg
France

Martine Queffélec
Mathématiques
Université de Lille
59655 Villeneuve d'Ascq Cédex
France

Abstract:

We investigate the rational approximation of the binary Thue-Morse-Mahler number. We prove that its continued fraction expansion has infinitely many partial quotients equal to 4 or 5 and infinitely many partial quotients greater than or equal to 50.

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(Concerned with sequences A004249 A010060 A014572.)

Received April 20 2012; revised version received June 6 2012. Published in Journal of Integer Sequences, March 2 2013.

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