OPEN
Let $g(n)$ be minimal such that there exists $A\subseteq \{0,\ldots,n\}$ of size $g(n)$ with $\{0,\ldots,n\}\subseteq A+A$. Estimate $g(n)$. In particular is it true that $g(n)\sim 2n^{1/2}$?
A problem of Rohrbach, who proved
\[(2^{1/2}+c)n^{1/2} \leq g(n) \leq 2n^{1/2}\]
for some small constant $c>0$.
