Hurwitz zeros escape

1. A.The sequence $(p_n)$ converges to an entire function uniformly on compact subsets of $\mathbb{C}$.
2. B.For all $n\ge 1,p_n$ has a zero in the set {$z\in \mathbb{C}$ : |z| ≤ 2023}.
3. C.There exists a sequence $(z_n)$ of complex numbers such that lim |$z_n$| $=\infty$ and $p_n(z_n)=0$ for all n ≥ 1.
4. D.Let $S_n$ be the set of all zeros of $p_n$. If $a_n=$ $mi{n}_{z\in S_n}$ |z|, then $a_n\to \infty$ as $n\to \infty$.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.