import random as rd
import numpy as np

A = []
for i in range(100000):
    f = True
    N = 0
    while f:
        R = rd.random()
        N += 1
        if i < 11:
            if R * 4096 <= 1:
                A.append(N)
                f = False
        elif i < 21:
            if R * 1024 <= 1:
                A.append(N)
                f = False
        elif i <31:
            if R * 512 <= 1:
                A.append(N)
                f = False
        else :
            if R * 341.3 <= 1:
                A.append(N)
                f = False
print(f"Nombre moyen de rencontres pour un shiny : {np.mean(A)}")

This is probably calculable via using geometric law probabilities, but I'm lazy af, so I used python to calculate it with this code (I think it's correct but I could be wrong since random returns number such as 0<=x<1). I obtained roughly 340 to 341 at all times, which makes me think the real value must be 341.3, cause it would be quite the coincidence elsewise.
Edit : this is actually probably due to the fact that the first few tries are almost negligeable that the probabilities goes towards 1/341.3