Journal of Integer Sequences, Vol. 29 (2026), Article 26.5.5

An Equidistribution Result for Differences Associated with Square Pyramidal Numbers


Anji Dong, Katerina Saettone, Kendra Song
Department of Mathematics
University of Illinois Urbana-Champaign
Urbana, IL 61801
USA

Alexandru Zaharescu
Department of Mathematics
University of Illinois Urbana-Champaign
Urbana, IL 61801
USA
and
Simion Stoilow Institute of Mathematics of the Romanian Academy
P. O. Box 1-764
RO-014700 Bucharest
Romania

Abstract:

We provide an asymptotic formula for the average value of the sequence A351830, whose terms are the absolute differences between square pyramidal numbers and their nearest perfect squares. Moreover, we supply asymptotic formulas for the k-th moment of this sequence of distances to the nearest perfect squares, for any fixed positive integer k.

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(Concerned with sequences A001032 A350886 A350887 A350888 A351830.)

Received October 8 2024; revised versions received December 24 2025; October 7 2026; October 8 2026. Published in Journal of Integer Sequences, October 8 2026.

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