Least k such that k*n and (k+1)*n fail to have a common nonzero digit

a308479.py

# This script calculates Sequence A0308479, the least k such that k*n and (k+1)*n 
# fail to have a common nonzero digit, or 0 if this property never occurs.
#
# See: https://oeis.org/A308479
#
# Author: David Radcliffe
# 9 June 2019

def share_digit(m, n):
    return set(str(m)) & set(str(n)) - set('0')
    
def a308479(n):
    m = len(str(n)) + 1
    for k in range(1, 10 ** m // n + 1):
        if not share_digit(k * n, (k + 1) * n):
            return k
    remainders = set()
    rem = pow(10, m, n)
    P = 10 ** m
    for p in range(m, m + n + 1):
        if rem in remainders:
            return 0
        remainders.add(rem)
        N = -1
        for a in range(1, 10):
            N += P
            k = N // n
            kn = k * n
            if not share_digit(kn, kn + n):
                return k
        rem = (10 * rem) % n
        P *= 10