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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 ≥ 1 let an be the smallest positive integer such that n + an is prime. We investigate the behavior of the sequence (an)n≥1, and prove asymptotic results for the sums ∑ n≤x an, ∑ n≤x 1/an, and ∑ n≤x log an.

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For every integer n ≥ 1 let an be the smallest positive integer such that n + an is prime. We investigate the behavior of the sequence (an)n≥1, and prove asymptotic results for the sums ∑ n≤x an, ∑ n≤x 1/an, and ∑ n≤x log an.

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Available abstract

For every integer n ≥ 1 let an be the smallest positive integer such that n + an is prime. We investigate the behavior of the sequence (an)n≥1, and prove asymptotic results for the sums ∑ n≤x an, ∑ n≤x 1/an, and ∑ n≤x log an.

Key concepts: Sequence (biology), Combinatorics, Integer (computer science), Prime (order theory), Mathematics, Prime factor, Prime number, Discrete mathematics

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