{
  "id": "2202.08986",
  "version": "v1",
  "published": "2022-02-18T02:28:01.000Z",
  "updated": "2022-02-18T02:28:01.000Z",
  "title": "The Fibonacci Sequence is Normal Base 10",
  "authors": [
    "Brennan Benfield",
    "Michelle Manes"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we show that the concatenation of the Fibonacci sequence is \\textit{normal} in base $10$, meaning every string of a given length, $k$, occurs as frequently as every other string of length $k$ (there are as many $1$'s as $2$'s and as many $704$'s and $808$'s). Although we know that almost every number is normal, we can name very few of them. It is still unclear if $e$, $\\pi$, or $\\sqrt{2}$ are normal. We show that concatenating the Fibonacci sequence behind a decimal creates a normal number in every base of the form $5^x\\times2^y$. We then provide evidence that potentially extends our result to all integer bases, and claim that the Fibonacci concatenation is \\textit{absolutely normal}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-18T02:28:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11B50"
    ],
    "keywords": [
      "fibonacci sequence",
      "normal base",
      "integer bases",
      "normal number",
      "decimal creates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}