A ${\mathbb N}$atural Avenue
Roberto Conti, Pierluigi Contucci
TL;DR
This paper explores an infinite sequence of rooted trees linked to number theory, examining their elementary properties and connections to classical number theory results and conjectures.
Contribution
It introduces and analyzes a new infinite sequence of rooted trees with properties related to fundamental number theory concepts.
Findings
Properties related to classical number theory results
Connections to number theory conjectures
Elementary structural insights into the sequence
Abstract
We consider an infinite sequence of rooted trees naturally emerging in a number-theoretical context. We advance some ideas on its structure by discussing some elementary properties. Some of those properties are shown to be related to classical results or conjectures in number theory.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Stochastic processes and statistical mechanics