If $S_n$ is a set of positive integers >0 of the least cardinality such that every positive integer less then $n$ can be written as the sum of at most two elements of $S_n$, how precisely can we bound the asymptotics of $|S_n|$ as $n\rightarrow\infty$ ?
And for $|S(n,k)|$, if every integer less then n can be written as the sum of at most k elements of $S(n,k)$?
And for $|G(n,k)|$, if every integer less then n can be written as the sum of exactly k elements of $G(n,k)$?
$S(n,2)$ = http://oeis.org/A082429