Define a list of number with the following properties:
- The first number of the list is a one-digit natural number.
- Each number (since the second) is obtained by adding $9$ to the number before in the list.
- The number $2012$ is in that list.
Find the first number of the list.
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:
\[
\boxed{5}
\]