{
  "id": "1903.11973",
  "version": "v1",
  "published": "2019-03-28T13:49:22.000Z",
  "updated": "2019-03-28T13:49:22.000Z",
  "title": "New computational results on a conjecture of Jacobsthal",
  "authors": [
    "Mario Ziller"
  ],
  "comment": "14 pages, 1 figure, 2 tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "Jacobsthal's conjecture has been disproved by counterexample a few years ago. We continue to verify this conjecture on a larger scale. For this purpose, we implemented an extension of the Greedy Permutation Algorithm and computed the maximum Jacobsthal function for the product of $k$ primes up to $k=43$. We have found various new counterexamples. Their pattern seems to imply that the conjecture of Jacobsthal only applies to several small $k$. Our results raise further questions for discussion. In addition to this paper, we provide exhaustive information about all covered sequences of the appropriate maximum lengths in ancillary files.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-28T13:49:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "computational results",
      "greedy permutation algorithm",
      "maximum jacobsthal function",
      "appropriate maximum lengths",
      "ancillary files"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}