{
  "id": "1309.7386",
  "version": "v1",
  "published": "2013-09-27T23:19:48.000Z",
  "updated": "2013-09-27T23:19:48.000Z",
  "title": "Some normal numbers generated by arithmetic functions",
  "authors": [
    "Paul Pollack",
    "Joseph Vandehey"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $g \\geq 2$. A real number is said to be g-normal if its base g expansion contains every finite sequence of digits with the expected limiting frequency. Let \\phi denote Euler's totient function, let \\sigma be the sum-of-divisors function, and let \\lambda be Carmichael's lambda-function. We show that if f is any function formed by composing \\phi, \\sigma, or \\lambda, then the number \\[ 0. f(1) f(2) f(3) \\dots \\] obtained by concatenating the base g digits of successive f-values is g-normal. We also prove the same result if the inputs 1, 2, 3, \\dots are replaced with the primes 2, 3, 5, \\dots. The proof is an adaptation of a method introduced by Copeland and Erdos in 1946 to prove the 10-normality of 0.235711131719\\ldots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-27T23:19:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K16"
    ],
    "keywords": [
      "normal numbers",
      "arithmetic functions",
      "denote eulers totient function",
      "sum-of-divisors function",
      "expansion contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7386P"
    }
  }
}