Gardado en:
| Autor Principal: | |
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| Formato: | Recurso digital |
| Idioma: | inglés |
| Publicado: |
Zenodo
2025
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| Subjects: | |
| Acceso en liña: | https://doi.org/10.5281/zenodo.15530664 |
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Table of Contents:
- <p>Several attempts have been made to generalize the Collatz sequence 3n+1, but<br>many of them produced sequences that lack the essential structural properties<br>of the original Collatz dynamics. Among these, the most promising known<br>generalization is the one proposed in 2022 by Naouel Boulkaboul [2], which<br>takes the form 3n + 3k and leads sequences to converge toward 3<br>k. In this work, we propose a new methodological generalization of the Collatz conjecture<br>based on the transformation (1 + 2k)n + Sk(n), where Sk(n) is a function<br>specifically designed to preserve the singularity and the core behavior of the<br>original sequence. We demonstrate that this generalization retains key features<br>such as singularity patterns and trivial cycles. Furthermore, we conduct a<br>computational verification for k = 1 to k = 42, supporting the conjecture that<br>all such generalized sequences converge to 1. This generalization opens the<br>door to new strategies for understanding and potentially proving the Collatz<br>conjecture in its broader form.</p>