Somme des chiffres et changement de base

2018/06/25 by de la Bretèche, Régis, Stoll, Thomas, Tenenbaum, Gérald
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1806.09670

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^∞. We also provide upper and lower bounds for the counting functions of the corresponding subsequences.

Related

• Finite generating functions for the sum of digits sequence
• The binary digits of n+t
• Approaching Cusick's Conjecture on the Sum-of-digits Function
• A lower bound for Cusick's conjecture on the digits of n+t
• Collisions of digit sums in bases 2 and 3