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

Bill Allombert 1, 2 Nicolas Brisebarre 3, 4 Alain Lasjaunias 1
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
3 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : 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.
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Bill Allombert, Nicolas Brisebarre, Alain Lasjaunias. On a two-valued sequence and related continued fractions in power series fields. The Ramanujan Journal, 2018, 45 (3), pp.859-871. ⟨10.1007/s11139-017-9892-7⟩. ⟨hal-01348576v3⟩

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