Problem 1356

1. Let $x$ be the first number in the list. According to the problem, each subsequent number in the list is obtained by adding $9$ to the previous number. Therefore, the numbers in the list form an arithmetic sequence with the first term $x$ and common difference $9$.

2. We are given that $2012$ is in the list. This means there exists some integer $n$ such that:
$$2012 = x + 9n$$
Rearranging this equation, we get:
$$2012 - x = 9n$$
This implies that $2012 - x$ must be divisible by $9$.

3. To find $x$, we need to determine the value of $x$ such that $2012 \equiv x \pmod{9}$. First, we calculate $2012 \mod 9$:
$$2012 = 2 + 0 + 1 + 2 = 5$$
Therefore:
$$2012 \equiv 5 \pmod{9}$$

4. Since $x$ is a one-digit natural number and $2012 \equiv x \pmod{9}$, the only single-digit natural number congruent to $2012 \pmod{9}$ is $5$. Thus, we have:
$$x = 5$$

Conclusion:
$$\boxed{5}$$