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

2 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2017

https://hal.archives-ouvertes.fr/hal-01348576
Contributeur : Nicolas Brisebarre <>
Soumis le : mardi 14 mars 2017 - 23:12:24
Dernière modification le : jeudi 15 juin 2017 - 09:09:12
Document(s) archivé(s) le : jeudi 15 juin 2017 - 15:13:40

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### Identifiants

• HAL Id : hal-01348576, version 3
• ARXIV : 1607.07235

### Citation

Bill Allombert, Nicolas Brisebarre, Alain Lasjaunias. On a two-valued sequence and related continued fractions in power series fields . 2017. <hal-01348576v3>

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