Number inequality in the Collatz equation and the solution of the equation

In this study, the trajectory behavior of odd numbers in the Collatz process is algebraically investigated using $k$ odd operations and $n$ even operations. The dependency relationship between parameters $k$ and $n$ and the resulting parity contradiction are examined through the inequality established for numbers assumed to be locked at a stop other than $1$.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-29
DOI
https://doi.org/10.5281/zenodo.23041918
Primary Topic
Benford’s Law and Fraud Detection
Type
article
Field-Weighted Citation Impact
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article

Number inequality in the Collatz equation and the solution of the equation

Alper Pektaş
Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
article

Number inequality in the Collatz equation and the solution of the equation

Alper Pektaş
article en

Abstract

In this study, the trajectory behavior of odd numbers in the Collatz process is algebraically investigated using $k$ odd operations and $n$ even operations. The dependency relationship between parameters $k$ and $n$ and the resulting parity contradiction are examined through the inequality established for numbers assumed to be locked at a stop other than $1$.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 8%
Benford’s Law and Fraud Detection
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Number inequality in the Collatz equation and the solution of the equation — Alper Pektaş · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS