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A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2 = 0.5

1/3 = 0.(3)

1/4 = 0.25

1/5 = 0.2

1/6 = 0.1(6)

1/7 = 0.(142857)

1/8 = 0.125

1/9 = 0.(1)

1/10 = 0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.



In [1]:

    
def cycle_len(N):
    n = 1
    ns = []
    while True:
        while n < N:
            n *= 10
        if n in ns:
            return len(ns)
        ns.append(n)
        
        n = n % N
        if n % N == 0:
            return 0

max_c, max_i = 0, 0
for i in range(1,1001):
    c = cycle_len(i)
    if c > max_c:
        max_c = c
        max_i = i
        print max_c, max_i



In [ ]: