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Some Properties of a Sequence Defined with the Aid of Prime Numbers
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Brăduţ Apostol

"Spiru Haret" Pedagogic High School

5 Timotei Cipariu St.

620004 Focşani

Romania

Laurenţiu Panaitopol

Lucian Petrescu

“Henri Coandă” Technical College

2 Tineretului St.

820235 Tulcea

Romania

László Tóth

Department of Mathematics

University of Pécs

Ifjúság útja 6

7624 Pécs

Hungary

**Abstract:**

For every integer *n* ≥ 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≥1},
and prove asymptotic results for the sums
Σ_{n≤x} *a*_{n},
Σ_{n≤x} 1/*a*_{n},
and Σ_{n≤x} log *a*_{n}.

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(Concerned with sequences
A000040
A001223
A013632
A076821.)

Received March 3 2015;
revised version received April 3 2015.
Published in *Journal of Integer Sequences*, May 21 2015.

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