The recursive function that models this question is: find f(32) given:
f(0) = 5
f(x) = f(x-1) + 2 ^ (f(x-1) + 1)
Explanation of the function:
f(0) = 5 because when the first AD comes into play it makes 2 PLs which is doubled to 4. 4 + 1 = 5. We are looking for f(32) because 2^5 ADs are created by Miirym because we have 5 PLs in play.
f(x) = f(x-1) + 2 ^ (f(x-1) + 1) because the number of PLs after each AD enters = Number of existing PLs + number of new PLs (2 ^ (f(x-1) + 1)). The number of new PLs is (2 ^ (f(x-1) + 1)) because AD creates 2 which is doubled a number of times = existing PLs
I plugged this function into Hypercalc at the suggestion of Gottfried Helms
The answer is 30 PT (3.553934904655 × 10^20)
Which means a power tower of 10s, 30 high with (3.553934904655 × 10^20) on top ie: 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^(3.553934904655 × 10^20)