Repeated concatenations in residue classes

TL;DR

This paper presents an algorithm to identify repeated concatenations of natural numbers within residue classes, inspired by a sequence of v-palindromes, and explores potential generalizations and variations of this concept.

Contribution

The paper introduces a novel algorithm for detecting repeated concatenations in residue classes and generalizes a sequence of v-palindromes, expanding the scope of related investigations.

Findings

Algorithm successfully identifies repeated concatenations in residue classes.

Generalization of v-palindrome sequences broadens the scope of the study.

Discussion of potential variations suggests avenues for future research.

Abstract

We give an algorithm to determine all the repeated concatenations, in a given base, of a natural number in a residue class. The author recently describes a particular sequence of $v$-palindromes that inspires this investigation. We also generalize this sequence and discuss how there could be variations of the investigation we do in this paper.