On a conjecture of Dekking: The sum of digits of even numbers

Original · EN

Let q≥ 2 and denote by sq the sum-of-digits function in base q. For j=0,1,...,q-1 consider # {0 ≤ n < N: sq(2n) ≡ j q }. In 1983, F. M. Dekking conjectured that this quantity is greater than N/q and, respectively, less than N/q for infinitely many N, thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.