{
  "id": "math/0610601",
  "version": "v1",
  "published": "2006-10-19T15:59:16.000Z",
  "updated": "2006-10-19T15:59:16.000Z",
  "title": "Regularity properties of the Stern enumeration of the rationals",
  "authors": [
    "Bruce Reznick"
  ],
  "comment": "Submitted for publication",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "The Stern sequence (s(n)) is defined by s(0) = 0, s(1) = 1, s(2n) = s(n), s(2n+1) = s(n) + s(n+1). Stern showed in 1858 that gcd(s(n),s(n+1)) = 1, and that for every pair of relatively prime positive integers (a,b), there exists a unique n so that s(n) = a and s(n+1) = b. We show that, in a strong sense, the average value of s(n)/s(n+1) is 3/2, and that for all d, (s(n),s(n+1)) is uniformly distributed among all feasible pairs of congruence classes modulo d. More precise results are presented for d = 2 and 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-19T15:59:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "11B37",
      "11B57",
      "11B75"
    ],
    "keywords": [
      "regularity properties",
      "stern enumeration",
      "congruence classes modulo",
      "precise results",
      "strong sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10601R"
    }
  }
}