The only fixed cycle for the binary representation of numbers in the Collatz conjecture is 1.

This lemma shows that 1 is the only fixed cycle in the binary representation of numbers under the Collatz mapping, with proof based on separation into left significant part and trailing zeros.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-02-23
DOI
https://doi.org/10.5281/zenodo.18745222
Primary Topic
Benford’s Law and Fraud Detection
Type
article
Field-Weighted Citation Impact
0.00
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article

The only fixed cycle for the binary representation of numbers in the Collatz conjecture is 1.

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

The only fixed cycle for the binary representation of numbers in the Collatz conjecture is 1.

Vitaly Reznik
article en

Abstract

This lemma shows that 1 is the only fixed cycle in the binary representation of numbers under the Collatz mapping, with proof based on separation into left significant part and trailing zeros.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 49%
Benford’s Law and Fraud Detection
DOIOpen Access PDFOpenAlex
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