{
  "id": "math/0512399",
  "version": "v2",
  "published": "2005-12-16T16:22:51.000Z",
  "updated": "2006-06-02T20:50:13.000Z",
  "title": "Summation of Series Defined by Counting Blocks of Digits",
  "authors": [
    "Jean-Paul Allouche",
    "Jeffrey Shallit",
    "Jonathan Sondow"
  ],
  "comment": "12 pages, Introduction expanded, references added, accepted by J. Number Theory",
  "journal": "Journal of Number Theory 123 (2007) 133-143",
  "doi": "10.1016/j.jnt.2006.06.001",
  "categories": [
    "math.NT"
  ],
  "abstract": "We discuss the summation of certain series defined by counting blocks of digits in the $B$-ary expansion of an integer. For example, if $s_2(n)$ denotes the sum of the base-2 digits of $n$, we show that $\\sum_{n \\geq 1} s_2(n)/(2n(2n+1)) = (\\gamma + \\log \\frac{4}{\\pi})/2$. We recover this previous result of Sondow in math.NT/0508042 and provide several generalizations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-02T20:50:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "11Y60"
    ],
    "keywords": [
      "counting blocks",
      "ary expansion",
      "generalizations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12399A"
    }
  }
}