An Analytical Approach to Exponent-Restricted Multiple Counting Sequences

TL;DR

This paper introduces and analyzes multiple-counting sequences, establishing recurrence relations, matrix representations, and connections to Fermat's little theorem, enhancing understanding of composite number distribution between bases.

Contribution

It presents new recurrent relationships, matrix forms, and generalized Binet formulas for multiple-counting sequences, linking them to fundamental number theory concepts.

Findings

Derived recurrence relations for multiple-counting sequences

Established matrix representations and generalized Binet formulas

Connected sequence properties to Fermat's little theorem and composite distribution

Abstract

This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I also studied matrix representations and obtained generalized Binet formulas for defined sequences. As a result of multiple-counting sequence explanation, this study leads to a better understanding for distribution of composite numbers between consecutive bases.