An Equidistribution Result for Differences Associated to Square Pyramidal Numbers II

TL;DR

This paper investigates the uniform distribution of the sequence measuring the distance from square pyramidal numbers to the nearest squares, extending the analysis to arithmetic progressions, and presents new theoretical results.

Contribution

It provides new equidistribution results for differences related to square pyramidal numbers and extends these findings to arithmetic progressions.

Findings

Established equidistribution properties for the sequence of differences.

Extended results to include arithmetic progressions.

Contributed new theoretical insights into number distribution patterns.

Abstract

This paper presents some new results concerned with uniform distribution properties associated with the sequence $(a_n)_{n\in\mathbb{N}}$, which is defined as the distance from the $n$-th square pyramidal number to the closest square. We also extend the results to arithmetic progressions.