Sur les entiers dont la somme des chiffres est moyenne

The goal of this paper is to study sets of integers with an average sum of digits. More precisely, let g be a fixed integer, s(n) be the sum of the digits of n in basis g. Let f:N→N such that, in any interval [gν,gν+1[, f(n) is constant and near from (g-1)ν/2. We give an asymptotic for the number of integers n