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

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.