On a family of 2-automatic sequences generating algebraic continued fractions in characteristic 2

TL;DR

This paper introduces a family of 2-automatic sequences constructed from periodic words that generate algebraic continued fractions specifically in characteristic 2, including the well-known period-doubling sequence.

Contribution

The paper presents a new family of automatic sequences that produce algebraic continued fractions in characteristic 2, expanding understanding of their structure and properties.

Findings

Includes the period-doubling sequence as a special case

Constructs sequences from ultimately periodic words

Demonstrates algebraic nature of the generated continued fractions

Abstract

We present family of automatic sequences that define algebraic continued fractions in characteristic 2. This family is constructed from ultimately period words and contains the period-doubling sequence.