{
  "id": "1906.08437",
  "version": "v1",
  "published": "2019-06-20T04:15:34.000Z",
  "updated": "2019-06-20T04:15:34.000Z",
  "title": "Base phi representations and golden mean beta-expansions",
  "authors": [
    "Michel Dekking"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In the base phi representation any natural number is written uniquely as a sum powers of the golden mean with digits 0 and 1, where one requires that the product of two consecutive digits is always 0. In this paper we give precise expressions for the those natural numbers for which the $k$th digit is 1, proving two conjectures for $k=0,1$. The expressions are all in terms of generalized Beatty sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-20T04:15:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B99"
    ],
    "keywords": [
      "base phi representation",
      "golden mean beta-expansions",
      "natural number",
      "generalized beatty sequences",
      "sum powers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}