import random
import math
import numpy as np
from collections import deque
import matplotlib.pyplot as plt
from matplotlib import mlab

def digits2number(digits):
    return int(''.join([str(d) for d in digits]))

X = []
for i in range (10000):
    unic_digits = deque(range(0, 10))
    num_len = 1 + math.floor(math.log(random.randint(1, 10000), 10))
    random.shuffle(unic_digits)
    if (unic_digits[0] == 0):
        unic_digits.rotate(1)
    X.append(digits2number(list(unic_digits)[:int(num_len)]))


plt.hist(X, 100, histtype='step', cumulative=True)