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1 IMB - Institut de Mathématiques de Bordeaux 2 ICJ - Institut Camille Jordan Villeurbanne 3 Statistics and Mathematics Unit 4 AG - Algèbre et géométrie

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

Author: Jean-Marc Deshouillers - Laurent Habsieger - Shanta Laishram - Bernard Landreau -



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