Increasing sequences with decreasing prime factors

Noah Lebowitz-Lockard
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 3, Pages 635–638
DOI: 10.7546/nntdm.2025.31.3.635-638
Full paper (PDF, 180 Kb)

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Authors and affiliations

Noah Lebowitz-Lockard
Department of Engineering, University of California, Irvine
Irvine, CA 92697, USA

Abstract

We bound the length of the longest sequence of increasing numbers for which their smallest prime factors form a decreasing sequence. While the upper bound is unconditional, the lower bound relies on a conjecture about prime gaps.

Keywords

• Increasing sequences
• Smallest prime factors

2020 Mathematics Subject Classification

• 11A05
• 11A41

References

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Manuscript history

• Received: 22 April 2025
• Revised: 14 September 2025
• Accepted: 16 September 2025
• Online First: 16 September 2025

Copyright information

Ⓒ 2025 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).