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Sums of the digits in bases 2 and 3

Jean-Marc Deshouillers 1 Laurent Habsieger 2 Shanta Laishram 3 Bernard Landreau 4 
1 IMB - Institut de Mathématiques de Bordeaux
2 CTN - Combinatoire, théorie des nombres
ICJ - Institut Camille Jordan [Villeurbanne]
3 Statistics and Mathematics Unit
4 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
Abstract : Let b ≥ 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 ≤ N : |s 3 (n) − s 2 (n)| ≤ 0.1457205 log n} > N 0.970359. The proof only uses the separate (or marginal) distributions of the values of s 2 (n) and s 3 (n).
Keywords : sums of digits expansion in bases 2 and 3
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Submitted on : Wednesday, November 23, 2016 - 9:18:04 PM
Last modification on : Saturday, December 4, 2021 - 3:42:07 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 4:56:08 AM

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  • HAL Id : hal-01401869, version 1
  • ARXIV : 1611.08180

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Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram, Bernard Landreau. Sums of the digits in bases 2 and 3. Number theory—Diophantine problems, uniform distribution and applications, Springer, pp.211-217, 2017. ⟨hal-01401869⟩

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