Publications and Preprints

Sums of the digits in bases $2$ and $3$
by
Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram and Bernard Landreau
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 $$\notag \Card \{n \le N : \left|s_3(n) - s_2(n)\right| \le 0.1457205 \log n \} \, > \, N^{0.970359}.$$ The proof only uses the separate (or marginal) distributions of the values of $s_2(n)$ and $s_3(n)$.

isid/ms/2016/13 [fulltext]