Problem 326

Erdős Problem #326: declared status 'open'. Formalized: yes. Let $A\subset \mathbb{N}$ be an additive basis of order $2$. Must there exist $B=\{b_1<b_2<\cdots\}\subseteq A$ which is also a basis such that$$\lim_{k\to \infty}\frac{b_k}{k^2}$$does not exist? Prize: no. Tags: additive basis, number theory.