7. (10 points) Observe the following sequence of numbers: $11,17,23,29,35, \cdots$ If starting from the $n$-th number, each number is greater than 2017, then $n=$ $\qquad$
【Analysis】Observe the following sequence of numbers: 11, 17, 23, 29, 35, $\cdots$
It can be seen that the rule is: the next number is 6 more than the previous one;
Find the $n$th number such that each number starting from the $n$th is greater than 2017, then $n=$.
【Solution】Solution: $11=5+6 \times 1$
$$
\begin{array}{l} 
17=5+6 \times 2 \\
23=5+6 \times 3 \\
29=5+6 \times 4 \\
\ldots
\end{array}
$$

The $n$th number $=5+6 \times n$
Therefore, we have: $5+6 n>2017$
$$
\begin{aligned}
6 n & >2012 \\
n & >335 \cdots 2
\end{aligned}
$$
$$
n=336 \text {; }
$$

Therefore, the answer is: 336.
【Comment】This is a problem involving the rule of an arithmetic sequence, finding the $n$th term of the sequence.