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Book Sections Year : 2017

Sums of the digits in bases 2 and 3, I

Abstract

Let b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the representationof an integer n in base b. For sufficiently large N , one has Card{n ≤ N : |s 3 (n) − s 2 (n)| ≤ 0.1457232 log n} > N 0.970359. The proof only uses the separate distributions of the values of s 2 (n) and s 3 (n).
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Dates and versions

hal-02480241 , version 1 (15-02-2020)

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  • HAL Id : hal-02480241 , version 1

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Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram, Bernard Landreau. Sums of the digits in bases 2 and 3, I. Number Theory - Diophantine Problems, Uniform Distribution and Applications, 2017. ⟨hal-02480241⟩
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