7. Find the pattern that the numerical sequence follows: $1,2,3,4,5,8,7,16,9 \ldots$, and write down the next five numbers.
7. Let's break down the given numerical sequence into two:

$$
1,3,5,7,9, \ldots \text { and } 2,4,8,16 \ldots
$$

Each term in the first sequence is obtained by adding two to the previous term, while each term in the second sequence is obtained by multiplying the previous term by two. Now, knowing the pattern, we can continue the sequence:

$$
1,2,3,4,5,8,7,16,9,32,11,64,13,128 \ldots
$$

Answer: $32,11,64,13,128$.