Work

Classification of Integers and Occurrence Patterns of Multiples of 3 in the Inverse Collatz Map

Year: 2026

Type: preprint

Abstract: We study the inverse map associated with the Collatz map, focusing on theconditions under which an inverse iterate is an integer and under which thatinteger is divisible by 3. We organize the exponent conditions according to aclassification of integers and use the periodicity of powers of 2 to examine theoccurrence of multiples of 3. Based on these results, we discuss the possibilityof cycles in the inverse map and state conjectures for future investigation.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23767961

Author: Niikura, Shota

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7224654796

Cites:

Cited by:

Related to: 10