English

Sums of the digits in bases 2 and 3

Number Theory 2016-11-28 v1

Abstract

Let b \ge 2 be an integer and let s b (n) denote the sum of the digits of the representation of an integer n in base b. For sufficiently large N , one has Card{n \le N : |s 3 (n) -- s 2 (n)| \le 0.1457205 log n} \textgreater{} N 0.970359. The proof only uses the separate (or marginal) distributions of the values of s 2 (n) and s 3 (n).

Keywords

Cite

@article{arxiv.1611.08180,
  title  = {Sums of the digits in bases 2 and 3},
  author = {Jean-Marc Deshouillers and Laurent Habsieger and Shanta Laishram and Bernard Landreau},
  journal= {arXiv preprint arXiv:1611.08180},
  year   = {2016}
}