Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.5

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


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 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 Σn≤x an,   Σn≤x 1/an,   and Σn≤x log an.

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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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