Problem 906

Erdős Problem #906: declared status 'open'. Formalized: yes. Is there an entire non-zero function $f:\mathbb{C}\to \mathbb{C}$ such that, for any infinite sequence $n_1<n_2<\cdots$, the set$$\{ z: f^{(n_k)}(z)=0 \textrm{ for some }k\geq 1\}$$is everywhere dense? Prize: no. Tags: analysis, iterated functions.