Iteration Steps of 3x + 1 Problem
Abstract
On the 3x + 1 problem, given a positive integer N, let D(N), O(N), and E(N) denote the total number of iteration steps, the number of odd iteration steps, and the number of even iteration steps, respectively, when N is iterated until it reaches 1. It is straightforward to observe that D(N)=O(N)+E(N). In this paper, we propose a conjecture termed the Weak Residue Conjecture (i.e., 2E(N)3O(N)·N
Fields of Study & Subjects
Benford’s Law and Fraud Detection
Analytic Number Theory Research
semigroups and automata theory
Publication details
- Journal / source
- The Fibonacci Quarterly
- Publisher
- Informa UK Limited
- Pages
- 1–14
- Publication date
- 6 August 2026
- Language
- EN