Erdős Problem 906

Reference: erdosproblems.com/906

theorem Erdos906.erdos_906 : sorry ↔ ∃ (f : ℂ → ℂ), Transcendental (Polynomial ℂ) f ∧ Differentiable ℂ f ∧ ∀ (n : ℕ → ℕ), StrictMono n → Dense {z : ℂ | ∃ (k : ℕ), iteratedDeriv (n k) f z = 0}

Does there exists an entire non-zero transcendental function f : ℂ → ℂ such that for any sequence n₀ < n₁ < ..., { z | ∃ k, iteratedDeriv (n k) f z = 0 } is dense.