A good number is defined as a natural number where each digit is 0 or 2. The number of natural numbers that are good numbers from 1 to n and not divisible by either 20 or 22 is defined as f(n). f(10^18) is calculated and output using an algorithm that efficiently finds f(n).

from collections import defaultdict
from collections import Counter
from itertools import accumulate

def f(n):
    c = Counter(str(n))
    return c["0"] + c["2"]

def f(n):
    return sum([f(int(i)) for i in str(n)])

def f(n):
    if n <= 1:
        return 0
    return f(n-1) + f(n-2)

def f(n):
    if n <= 1:
        return 0
    elif n == 2:
        return 1
    else:
        return f(n-1) + f(n-2)

def f(n):
    if n <= 1:
        return 0
    a = 1
    b = 1
    for i in range(n-2):
        c = a + b
        a = b
        b = c
    return c

def f(n):
    if n <= 1:
        return 0
    a = 1
    b = 1
    for i in