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

2016/07/25 by Allombert, Bill, Brisebarre, Nicolas, Lasjaunias, Alain
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1607.07235

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 \mathbbF_3, which satisfies a simple algebraic equation of degree 4, introduced thirty years ago by D. Robbins.

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