Magic 123

Start with a number and count the number E of even and the number O of odd digits. Let's say you pick the number 7397418. E=2 and O=5,

Write them down next to each other following by their sum E + O. So the new number is 257.

Treat the result as a new number and continue the process. So 257 becomes 123. 123 becomes 123.

In this example, iterations converge very rapidly. Moreover, in just a few steps they reach the number 123 which has exactly 3 digits of which 1 is even and two are odd. Therefore, applying the computations to 123 produces the number 123 itself, such that further iterations become really mindless. Of course we can always start with another number.