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arXiv · 1503.01086

Some properties of a sequence defined with the aid of prime numbers

Brăduţ Apostol·Laurenţiu Panaitopol·Lucian Petrescu·László Tóth
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Abstract

For every integer $n\ge 1$ let $a_n$ be the smallest positive integer such that $n+a_n$ is prime. We investigate the behavior of the sequence $(a_n)_{n\ge 1}$, and prove asymptotic results for the sums $\sum_{n\le x} a_n$, $\sum_{n\le x} 1/a_n$ and $\sum_{n\le x} \log a_n$.

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Brăduţ Apostol, Laurenţiu Panaitopol, Lucian Petrescu, László Tóth. 2015-03-03. Some properties of a sequence defined with the aid of prime numbers. https://arxiv.org/abs/1503.01086

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