{
  "id": "2301.13563",
  "version": "v1",
  "published": "2023-01-31T11:22:01.000Z",
  "updated": "2023-01-31T11:22:01.000Z",
  "title": "The Thue-Morse sequence in base 3/2",
  "authors": [
    "Michel Dekking"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We discuss the base 3/2 representation of the natural numbers. We prove that the sum of digits function of the representation is a fixed point of a 2-block substitution on an infinite alphabet, and that this implies that sum of digits function modulo 2 of the representation is a fixed point $x_{3/2}$ of a 2-block substitution on $\\{0,1\\}$. We prove that $x_{3/2}$ is mirror invariant, and present a list of conjectured properties of $x_{3/2}$, which we think will be hard to prove. Finally, we make a comparison with a variant of the base 3/2 representation, and give a general result on $p$-$q$-block substitutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-31T11:22:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B85",
      "68R15"
    ],
    "keywords": [
      "thue-morse sequence",
      "representation",
      "fixed point",
      "digits function modulo",
      "block substitutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}