SOLVED

Let $(S_n)_{n\geq 1}$ be a sequence of sets of complex numbers, none of which have a finite limit point. Does there exist an entire function $f(z)$ such that, for all $n\geq 1$, there exists some $k_n\geq 0$ such that
\[f^{(k_n)}(z) = 0\textrm{ for all }z\in S_n?\]

Solved in the affirmative by Barth and Schneider [BaSc72].