Iterative calculation values in the Collatz conjecture eventually reach 1 as if walking across tightropes: Physical meaning of the ratio R

The ratio R, defined as the ratio of the number of even integers to the number of odd integers minus one that appear in the iterative process of the Collatz conjecture, can serve as a criterion for determining whether the iterated values eventually reach 1. This paper explains the physical meaning of R from the perspective of tightrope walking along Collatz ropes.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23938488
Primary Topic
Smarandache Functions and Recreational Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

Iterative calculation values in the Collatz conjecture eventually reach 1 as if walking across tightropes: Physical meaning of the ratio R

Fumihidé Shiraishi
Zenodo (CERN European Organization for Nuclear Research)
Smarandache Functions and Recreational Number Theory
article

Iterative calculation values in the Collatz conjecture eventually reach 1 as if walking across tightropes: Physical meaning of the ratio R

Fumihidé Shiraishi
article en

Abstract

The ratio R, defined as the ratio of the number of even integers to the number of odd integers minus one that appear in the iterative process of the Collatz conjecture, can serve as a criterion for determining whether the iterated values eventually reach 1. This paper explains the physical meaning of R from the perspective of tightrope walking along Collatz ropes.

Zenodo (CERN European Organization for Nuclear Research)
Kyushu University (JP)
Openalex Percentile: Top 11%
Smarandache Functions and Recreational Number Theory
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