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arXiv · 1305.1017

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

Iurie Boreico·Daniel El-Baz·Thomas Stoll
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Abstract

Let $q\geq 2$ and denote by $s_q$ the sum-of-digits function in base $q$. For $j=0,1,...,q-1$ consider $$# \{0 \le n < N : \;\;s_q(2n) \equiv j \pmod q \}.$$ 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.

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Iurie Boreico, Daniel El-Baz, Thomas Stoll. 2013-05-08. On a conjecture of Dekking : The sum of digits of even numbers. https://arxiv.org/abs/1305.1017

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