The affirmative solution to the Waring problem says that every $A_k = \{n^k|n\in \mathbb{N}\}$ is an additive basis for any choice of $k$.
Of course, $B_k = \{k^n| n \in \mathbb{N}\}$ is not an additive basis since there are integers with arbitrarily long representations base $k$.
My question is about sets with intermediate/sub-exponential growth. Namely, is $C = \{ \lfloor n^{\log n} \rfloor | n \in \mathbb{N} \}$ an additive basis?
