A sequence of integers $a_{1}, a_{2}, \cdots$ is called $good$ if: • $a_{1}=1$, and; • $a_{i+1}-a_{i}$ is either $1$ or $2$ for all $i \geq 1$. Find all positive integers n that cannot be written as a sum $n = a_{1} + a_{2} + \cdots + a_{k}$, such that the integers $a_{1} , a_{2} , \cdots , a_{k}$ forms a good sequence.