{
  "id": "2404.14765",
  "version": "v1",
  "published": "2024-04-23T06:02:04.000Z",
  "updated": "2024-04-23T06:02:04.000Z",
  "title": "On the order of magnitude of certain integer sequences",
  "authors": [
    "Michael Hellus",
    "Anton Rechenauer",
    "Rolf Waldi"
  ],
  "comment": "11 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime number, and let $S$ be the numerical semigroup generated by the prime numbers not less than $p$. We compare the orders of magnitude of some invariants of $S$ with each other, e. g., the biggest atom $u$ of $S$ with $p$ itself: By Harald Helfgott (arXiv:1312.7748 [math.NT]), every odd integer $N$ greater than five can be written as the sum of three prime numbers. There is numerical evidence suggesting that the summands of $N$ always can be chosen between $\\frac N6$ and $\\frac N2$. This would imply that $u$ is less than $6p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-23T06:02:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D07",
      "20M14"
    ],
    "keywords": [
      "integer sequences",
      "prime number",
      "biggest atom",
      "harald helfgott",
      "odd integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}