Sums of the Digits in Bases 2 and 3

Jean-Marc Deshouillers (), Laurent Habsieger (), Shanta Laishram () and Bernard Landreau ()
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Jean-Marc Deshouillers: Bordeaux INP, Université de Bordeaux, CNRS, Institut Mathématique de Bordeaux, UMR 5251
Laurent Habsieger: Université de Lyon, CNRS UMR 5208, Institut Camille Jordan
Shanta Laishram: Indian Statistical Institute
Bernard Landreau: Université d’Angers, CNRS, LAREMA Laboratoire Angevin de REcherche en MAthématiques, UMR 6093, FR 2962

A chapter in Number Theory – Diophantine Problems, Uniform Distribution and Applications, 2017, pp 211-217 from Springer

Abstract: 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 . $$\displaystyle{\mathop{\mathrm{Card}}\nolimits \{n \leq N: \left \vert s_{3}(n) - s_{2}(n)\right \vert \leq 0.1457205\log n\}\,>\, N^{0.970359}.}$$ The proof only uses the separate (or marginal) distributions of the values of s 2(n) and s 3(n).

Keywords: 11K16 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-55357-3_9

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