An explicit economical additive basis

Abstract

We present an explicit subset $A\subseteq \mathbb{N}=\{0,1,\dots \}$ such that $A+A=\mathbb{N}$ and for all $\epsilon >0$, \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big\}\big|}{N^{\varepsilon}} = 0.\] This answers a question of Erdős.

5 pages