keyseq.py

# chl, 2010-04-27
# http://blog.tech.stylefeeder.com/2008/05/27/generating-primary-keys/

import math

NUM = "0123456789"
LOWER = "abcdefghijklmnopqrstuvwxyz"
UPPER = LOWER.upper()
ALPHANUM = NUM + LOWER + UPPER
ASCII_94 = [chr(33 + x) for x in xrange(94)]

def is_prime(n):
    if n < 2:
        return False
    for x in xrange(2, int(math.sqrt(n)) + 1):
        if n % x == 0:
            return False
    return True

def next_prime(x):
    while not is_prime(x):
        x += 1
    return x

def _base(x, b):
    while x:
        yield x % b
        x //= b

def base(x, b):
    return list(reversed(list(_base(x, b))))

def _keyseq(n, k, c=0):
    while True:
        yield c
        c = (c + k) % n

def keyseq(alphabet=ALPHANUM, length=5, start=0):
    a = len(alphabet)
    n = a ** length
    # determine k co-prime to n
    p, k = next_prime(a + 1), 1
    while k < n:
        p = next_prime(p + 1)
        k = p * k
    return ("".join(alphabet[d] for d in base(x, a)).rjust(length, alphabet[0]) for x in _keyseq(n, k, int(start % n)))