Somme des chiffres et changement de base  [ Sum of digits and change of base ]
Annales de l'Institut Fourier, Volume 69 (2019) no. 6, p. 2507-2518

For q2, let s q (n) denote the sum of digits of an integer n in the base q expansion. Answering, in an 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.

Pour q2, soit s q (n) la somme des chiffres d’un entier n en base q. Répondant, sous une forme étendue, à une question de Deshouillers, Habsieger, Laishram, et Landreau, nous montrons que, dès que a et b sont multiplicativement indépendants, tout nombre réel positif est valeur d’adhérence de la suite {s b (n)/s a (n)} n=1 . Nous donnons également un encadrement des fonctions de comptage des sous-suites associées.

Received : 2018-06-20
Revised : 2018-10-16
Accepted : 2019-01-17
Published online : 2019-10-29
DOI : https://doi.org/10.5802/aif.3300
Classification:  11A63,  11K16,  11K60,  11J82
Keywords: sum of digits, multiplicative independence, exponent of irrationality, binomial recentering
@article{AIF_2019__69_6_2507_0,
     author = {de la Bret\`eche, R\'egis and Stoll, Thomas and Tenenbaum, G\'erald},
     title = {Somme des chiffres et changement de base},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {69},
     number = {6},
     year = {2019},
     pages = {2507-2518},
     doi = {10.5802/aif.3300},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_2019__69_6_2507_0}
}
Somme des chiffres et changement de base. Annales de l'Institut Fourier, Volume 69 (2019) no. 6, pp. 2507-2518. doi : 10.5802/aif.3300. https://aif.centre-mersenne.org/item/AIF_2019__69_6_2507_0/

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