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.

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