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For every integer $n\ge 1$ let $a_n$ be the smallest positive integer suchthat $n+a_n$ is prime. We investigate the behavior of the sequence $(a_n)_{n\ge1}$, and prove asymptotic results for the sums $\sum_{n\le x} a_n$, $\sum_{n\lex} 1/a_n$ and $\sum_{n\le x} \log a_n$.

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