On sequences without geometric progressions

TL;DR

This paper improves the upper bound on the density of positive integer sequences that avoid containing any k-term geometric progressions, advancing understanding of their structure and limitations.

Contribution

It provides a tighter upper bound for the density of sequences without k-term geometric progressions, refining previous results.

Findings

Established a new upper bound for sequence density

Enhanced understanding of geometric progression-free sequences

Contributed to combinatorial number theory

Abstract

An improved upper bound is obtained for the density of sequences of positive integers that contain no k-term geometric progression.