4. Let $S$ be the set of integers that can be written in the form $50 m+3 n$ where $m$ and $n$ are non-negative integers. For example 3, 50, 53 are all in $S$. Find the sum of all positive integers not in $S$.
4. If $x$ is the smallest integer in $S$ such that $x \equiv i(\bmod 3)$, then $x+3 k \in S$ and $x-3(k+1) \notin S$ for all $k \geq 0$. We have 3 is the smallest multiple of 3 that is in $S ; 50$ is smallest number in $S$ that is $\equiv 2(\bmod 3)$ and 100 is the smallest number in $S$ that is $-1(\bmod 3)$. Thus the positive numbers not in $S$ are $1,4, \ldots, 97$ and $2,5, \ldots, 47$. Their sum is
$$
\frac{33(97+1)}{2}+\frac{16(2+47)}{2}=2009 .
$$