To find the number of integers in an arithmetic sequence, I need to know the first term, the common difference, and the last term. The first term is 13, the common difference is 20 - 13 = 7, and the last term is 2008. The general formula for the n-th term of an arithmetic sequence is $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, $d$ is the common difference, and $a_n$ is the n-th term. I can use this formula to find the value of n that corresponds to the last term, 2008. Plugging in the values, I get $2008 = 13 + (n-1)7$. Simplifying, I get $1995 = 7(n-1)$. Dividing by 7, I get $285 = n-1$. Adding 1, I get $n = 286$. This means there are 286 terms in the arithmetic sequence from 13 to 2008. 
How many integers belong to the arithmetic sequence 13, 20, 27, 34, $\dots$, 2008?