Even, Odd and Total Number of Digits

Start with a number and count the number E of even and the number O of odd digits. Write them down next to each other following by their sum E + O. Treat the result as a new number and continue the process. 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.

(In the applet below, most of the numbers are clickable so that you can change their values. The starting number may be looked at as a string of individual digits or as a long number depending on whether the Autonomous digits button is checked or unchecked.)

Why is it always 123?

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