Modular Map of Collatz Sequence and Its Implications

EasyChair Preprint 2639

Abstract

Let C:N+1→N+1 and C(n)= n/2 if n is even and C(n)=3n+1 if n is odd for all n ∈ N + 1. The Collatz Conjecture states that there exists a finite number k such that C^{k}(n) = 1. In this paper, a modular map of Collatz sequence and several implications are presented, which serve as insights into the further analysis of the Collatz Conjecture.

Keyphrases: Collatz Conjecture, modular arithmetic, number theory

@booklet{EasyChair:2639,
  author    = {Binh Ho},
  title     = {Modular Map of Collatz Sequence and Its Implications},
  howpublished = {EasyChair Preprint 2639},
  year      = {EasyChair, 2020}}