{
  "id": "1908.03855",
  "version": "v1",
  "published": "2019-08-11T05:15:13.000Z",
  "updated": "2019-08-11T05:15:13.000Z",
  "title": "New Transcendental Numbers from Certain Sequences",
  "authors": [
    "Hung Viet Chu"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We construct three infinite decimals from certain digits of $n^n, n^m$, and $(n!)^m$ (for any fixed $m$) and show that all three are transcendental. In particular, while previous work looked at the last non-zero digit of $n^n$, we look at the digit right before its last non-zero digit. Secondly, we prove the transcendence of the infinite decimal from the last non-zero digit of $n^{4m}$. Finally, we generalize Dresden's result by showing that the decimal from $(n!)^m$ ($m$ not divisible by $4$) is also transcendental. We end with a list of questions for future research.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-11T05:15:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B83"
    ],
    "keywords": [
      "transcendental numbers",
      "non-zero digit",
      "infinite decimal",
      "digit right",
      "generalize dresdens result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}