Given n, find k such that first n digits of 2^k == first n digits of 5^k == first n digits of sqrt(10)

main.py

digits = "31622776601683795"

def find(n):
    k = 0
    last_2 = 1
    last_5 = 1
    while True:
        if first_n_digits(last_2, n) == digits[:n] \
        and first_n_digits(last_5, n) == digits[:n]:
            return k
        last_2 *= 2
        last_5 *= 5
        k+=1
        print(k)

def first_n_digits(n, n_digits):
    n_string = f'{n}'
    if len(n_string) < n_digits:
        return n_string
    return n_string[:n_digits]

def main():
    print(find(5))

main()