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arXiv · 1607.07235

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

Bill Allombert·Nicolas Brisebarre·Alain Lasjaunias
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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. 2016-07-25. On a two-valued sequence and related continued fractions in power series fields. https://arxiv.org/abs/1607.07235

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