Let b $\ge$ 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 $\le$ N : |s 3 (n) -- s 2 (n)| $\le$ 0.1457205 log n} \textgreater{ } N 0.970359. The proof only uses the separate (or marginal) distributions of the values of s 2 (n) and s 3 (n).
Categories: math.NT