class infinitelist(object):
    #allows a list to be accessed infinitely, where indexes beyond it's length are reduced to match an index.
    def __init__(self, lst):
        self.lst = lst
    def __repr__(self):
        return str(self.lst)
    def __len__(self):
        return len(self.lst)
    def __getitem__(self, i):
        if i == len(self.lst):
            return self.lst[i%len(self.lst)]
        elif i > len(self.lst)-1:
            return self.lst[i%len(self.lst)-1]
        else:
            return self.lst[i]


def num_hash(i):
    chars = ['a', 'b', 'c', 'd',
    'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm',
    'n', 'o', 'p', 'q', 'r', 's',
    't', 'u', 'v', 'w', 'x', 'y', 'z', '0', '1', '2',
    '3', '4', '5', '6', '7', '8', '9']
    selection = infinitelist([x+y for x in chars for y in chars])
    hashed = ''
    while len(hashed) < 16:
        if i % 2 == 0:
            hashed += selection[i]
            i *= 4
        elif len(hashed) % 2 == 0:
            hashed += selection[i+4]
            i *= 3
        else:
            hashed += selection[i+1]
            i += 8
    return hashed