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

TL;DR

This paper constructs a notable transcendental continued fraction in power series fields over Q, linked to a specific {1, 2} sequence, with an irrationality measure of 3, originating from Robbins' algebraic continued fraction over .

Contribution

It explicitly describes a transcendental continued fraction in power series fields with a specific irrationality measure, connected to Robbins' algebraic continued fraction.

Findings

Explicit description of a transcendental continued fraction with irrationality measure 3

Connection between the continued fraction and a sequence in {1, 2}

Relation to Robbins' algebraic continued fraction over 

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.