Lukas Spiegelhofer, Montanuniversität Leoben, Leoben, Autriche

Collisions of digit sums in different bases

We study the sum-of-digits function s_q in integer base q ≥ 2. The expected values of s₂ and s₃ on [N,2N)
differ by >> ε log N for some ε > 0, and the standard deviations are small compared to this difference.
Consequently, not too many "collisions" ---integers n such that s₂(n) = s₃(n)--- can be expected. We
prove that there are infinitely many collisions of the binary and the ternary sum-of-digits functions,
thereby settling a folklore conjecture.