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arXiv · 1806.09670

Somme des chiffres et changement de base

Régis de la Bretèche·Thomas Stoll·Gérald Tenenbaum
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Abstract

Let $s_a(n)$ denote the sum of digits of an integer $n$ in the base $a$ expansion. Answering, in a extended form, a question of Deshouillers, Habsieger, Laishram, and Landreau, we show that, provided $a$ and $b$ are multiplicatively independent, any positive real number is a limit point of the sequence $\{s_b(n)/s_a(n)\}_{n=1}^{\infty}$. We also provide upper and lower bounds for the counting functions of the corresponding subsequences.

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Régis de la Bretèche, Thomas Stoll, Gérald Tenenbaum. 2018-06-25. Somme des chiffres et changement de base. https://arxiv.org/abs/1806.09670

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