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Book Sections Year : 2017

Sums of the digits in bases 2 and 3


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).
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hal-01401869 , version 1 (23-11-2016)



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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