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