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

Brăduţ Apostol, Laurenţiu Panaitopol, Lucian Petrescu, László Tóth

Published 2015-03-03Version 1

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 $\sum_{n\le x} \log a_n$.