{
  "id": "0907.0880",
  "version": "v7",
  "published": "2009-07-05T19:02:04.000Z",
  "updated": "2012-10-08T13:55:09.000Z",
  "title": "Equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x)$ for Thue-Morse sequence",
  "authors": [
    "Vladimir Shevelev"
  ],
  "comment": "14 pages. Adding in proof of Theorem 2 in detail point 5",
  "categories": [
    "math.NT"
  ],
  "abstract": "For every $a\\geq1$ we give a recursion algorithm of building of set of solutions of equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x),$ where $\\{t(n)\\}$ is Thue-Morse sequence. We pose an open problem and two conjectures.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2012-10-08T13:55:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B83"
    ],
    "keywords": [
      "thue-morse sequence",
      "recursion algorithm",
      "open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0880S"
    }
  }
}