Showcase of math phenomenon where multiples of b-1 having a predictable pattern in base b

mul-table of b-1 in radix b.py

#!/usr/bin/env python3
from typing import Final
from string import digits, ascii_letters

from sys import argv

FULL_CHARSET: Final = digits + ascii_letters


def to_radix(n: int, charset='0123456789', lil_endian=False):
	'''
	convert to base `len(charset)`
	'''

	radix = len(charset)

	out = ''
	while True:
		if lil_endian:
			out += charset[n % radix]
		else:  # big-endian
			out = charset[n % radix] + out
		n //= radix
		if n == 0:
			break
	return out


def main(*args: str):
	radix: Final = int(args[0]) if len(args) > 0 else 10

	if radix < 1 or radix > len(FULL_CHARSET):
		raise ValueError(f'unsupported radix: {radix}')

	for i in range(radix):
		print(to_radix(i * (radix - 1), FULL_CHARSET[:radix]))


if __name__ == '__main__':
	main(*argv[1:])