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arXiv · 2412.10097

An Equidistribution Result for Differences Associated with Square Pyramidal Numbers

Anji Dong·Katerina Saettone·Kendra Song·Alexandru Zaharescu
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Abstract

We provide an asymptotic formula for the average value of the sequence A351830: $a_{n} = |P_{n} - y^{2}_{n}|$ for $1 \leq n \leq x$, where $P_{n}$ is the $n$-th square pyramidal number and $y^{2}_{n}$ is the closest square to $P_{n}$. Moreover, we supply asymptotic formulas for the $k$-th moment of the same sequence, for any fixed natural number $k$.

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Anji Dong, Katerina Saettone, Kendra Song, Alexandru Zaharescu. 2024-12-13. An Equidistribution Result for Differences Associated with Square Pyramidal Numbers. https://arxiv.org/abs/2412.10097

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