Sequence pairs related to produced graphs from a method for dividing a natural number by two

TL;DR

This paper introduces MS-pairs generated through an algorithm dividing natural numbers by two, exploring their properties like unpredictability and chaos, with potential applications in complex systems.

Contribution

It presents a novel method for creating MS-pairs from division algorithms and analyzes their interesting dynamic properties.

Findings

MS-pairs exhibit unpredictability and chaos

Related graphs show irreversible and aperiodic behavior

Potential applications in complex systems and cryptography

Abstract

This paper is about producing a new kind of the pairs which we call it MS-pairs. To produce these pairs, we use an algorithm for dividing a natural number $x$ by two for two arbitrary numbers and consider their related graphs. We present some applications of these pairs that show their interesting properties such as unpredictability, irreversible, aperiodicity and chaotic behavior.