### Numbers, exponents and cycles

Suppose we have a number $N_0$. We apply the following procedure to $N_0$ in order to obtain a new number $N_1$: we take $N_0$‘s digits and raise them alternatively to 2 and 4, summing the results. Thus, $N_0=2435$ will become $N_1=2^4+4^2+3^4+5^2=138$. We don’t stop here. Instead, we apply the same procedure to $N_1$ obtaining $N_2=1^2+3^4+8^2=146$.

Of course, and someone can prove it, this procedure will quickly lead either to a number already seen or to 1. For now, we are only interested in the number of iterations required for this.