{
  "id": "1503.01086",
  "version": "v1",
  "published": "2015-03-03T20:07:48.000Z",
  "updated": "2015-03-03T20:07:48.000Z",
  "title": "Some properties of a sequence defined with the aid of prime numbers",
  "authors": [
    "Brăduţ Apostol",
    "Laurenţiu Panaitopol",
    "Lucian Petrescu",
    "László Tóth"
  ],
  "comment": "7 pages; This research was initiated by Lauren\\c{t}iu Panaitopol (1940--2008), former professor at the Faculty of Mathematics, University of Bucharest, Romania. The present paper is dedicated to his memory",
  "categories": [
    "math.NT"
  ],
  "abstract": "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 $\\sum_{n\\le x} \\log a_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-03T20:07:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A41",
      "11N05"
    ],
    "keywords": [
      "prime numbers",
      "properties",
      "asymptotic results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150301086A"
    }
  }
}