{
  "id": "1712.08666",
  "version": "v1",
  "published": "2017-12-22T21:26:37.000Z",
  "updated": "2017-12-22T21:26:37.000Z",
  "title": "Modular periodicity of the Euler numbers and a sequence by Arnold",
  "authors": [
    "Sanjay Ramassamy"
  ],
  "comment": "6 pages, 2 figures, 1 table",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "For any positive integer $q$, the sequence of the Euler up/down numbers reduced modulo $q$ was proved to be ultimately periodic by Knuth and Buckholtz. Based on computer simulations, we state for each value of $q$ precise conjectures for the minimal period and for the position at which the sequence starts being periodic. When $q$ is a power of $2$, a sequence defined by Arnold appears, and we formulate a conjecture for a simple computation of this sequence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-22T21:26:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euler numbers",
      "modular periodicity",
      "euler up/down numbers reduced modulo",
      "computer simulations",
      "precise conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}