Direct definition of a ternary infinite square-free sequence

TL;DR

This paper introduces a new ternary infinite square-free sequence, defined by an iterative process and a finite automaton, extending the concept of automatic sequences like Thue-Morse.

Contribution

It presents a novel ternary square-free sequence with both iterative and automaton-based direct definitions, expanding the class of automatic sequences.

Findings

Sequence is infinite and square-free.

Sequence is generated by a finite automaton.

Sequence is analogous to Thue-Morse in structure.

Abstract

We propose a new ternary infinite (even full-infinite) square-free sequence. The sequence is defined both by an iterative method and by a direct definition. Both definitions are analogous to those of the Thue-Morse sequence. The direct definition is given by a deterministic finite automaton with output. In short, the sequence is automatic.