Erdős Problem #14 — Sequences where almost all $n$ have exactly one sum representation

Now I state a few problems of Nathanson and myself : Let $a_1 < a_2 < \cdots$ be an infinite sequence of integers; denote by $f(n)$ the number of solutions of $n = a_i + a_j$. Denote by $B(x)$ the number of integers $n < x$ for which $f(n) \neq 1$ i.e. $B(x)$ is the number of integers for which $f(n) = 0$ or $f(n) > 1$. It is not hard to show that there is a sequence $A$ for which $B(x) = o(x^{\frac{1}{2}+\epsilon})$ We conjectured that

$$\frac{B(x)}{x^{1/2}} \to 0$$