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$$\{z:f^{(n_k)}(z)=0\text{ for some }k\ge 1\}$$is everywhere dense?

AMS 30 · open (literature)

theorem erdos_906 : answer(sorry) ↔ ∃ f : ℂ → ℂ, Transcendental (Polynomial ℂ) f ∧
    Differentiable ℂ f ∧ ∀ n : ℕ → ℕ, StrictMono n →
    Dense { z | ∃ k, iteratedDeriv (n k) f z = 0 }