ALLOMBERT, Bill; BRISEBARRE, Nicolas; LASJAUNIAS, Alain

doi:10.1007/s11139-017-9892-7

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ALLOMBERT, Bill
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]

BRISEBARRE, Nicolas
Arithmetic and Computing [ARIC]
Laboratoire de l'Informatique du Parallélisme [LIP]

LASJAUNIAS, Alain
Institut de Mathématiques de Bordeaux [IMB]

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Ramanujan Journal. 2018, vol. 45, n° 3, p. 859-871

Springer Verlag

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We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. This continued fraction is a generating function of a particular sequence in the set {1, 2}. The origin of this sequence, whose study was initiated in a recent paper, is to be found in another continued fraction, in the field of power series over $\mathbb{F}_3$, which satisfies a simple algebraic equation of degree 4, introduced thirty years ago by D. Robbins.< Leer menos

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power series over a finite field

finite alphabet

finite automata

formal power series

continued fractions

words

automatic sequences

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On a two-valued sequence and related continued fractions in power series fields

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