Increasing sequences with decreasing prime factors

We bound the length of the longest sequence of increasing numbers ≤ x 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.

Authors

Institutions

Publication Details

Journal
Notes on Number Theory and Discrete Mathematics
Published
2025-01-01
DOI
https://doi.org/10.7546/nntdm.2025.31.3.635-638
Primary Topic
Rings, Modules, and Algebras
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Increasing sequences with decreasing prime factors

Noah Lebowitz-Lockard
Notes on Number Theory and Discrete Mathematics
Rings, Modules, and Algebras
article

Increasing sequences with decreasing prime factors

Noah Lebowitz-Lockard
article en

Abstract

We bound the length of the longest sequence of increasing numbers ≤ x 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.

Notes on Number Theory and Discrete MathematicsVol. 31(3)
University of California, Irvine (US), Irvine University (US)
Openalex Percentile: Top 68%
Rings, Modules, and Algebras
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Increasing sequences with decreasing prime factors — Noah Lebowitz-Lockard · Notes on Number Theory and Discrete Mathematics (2025) | TGRS Research Map | TGRS