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Python

from math import prod
from sympy.ntheory.digits import digits
def mp(n, b): # multiplicative persistence of n in base b [from Michael S. Branicky in A330152]
    c = 0
    while n >= b:
        n, c = prod(digits(n, b)[1:]), c+1
    return c
def a(n):
    k = 0
    while True:
        if b := next((b for b in range(2, max(3, k)) if mp(k, b)==n), 0): return b
        k += 1
print([a(n) for n in range(11)])