On sequences of integers with small prime factors

TL;DR

This paper investigates sequences of integers with small prime factors, demonstrating that the gap between consecutive terms increases without bound as the greatest prime factor grows slowly.

Contribution

It establishes a new result linking the growth of the greatest prime factor to the unbounded difference between consecutive sequence terms.

Findings

Difference between consecutive terms tends to infinity

Sequences with slowly growing prime factors have unbounded gaps

Provides insight into the structure of integers with small prime factors

Abstract

We show that the difference between consecutive terms in sequences of integers whose greatest prime factor grows slowly tends to infinity.