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 decimal_period(n):
while n % 2 == 0:
n //= 2
while n % 5 == 0:
n //= 5
if n == 1:
return 0
k = 10 % n
p = 1
while k != 1:
k = (10*k) % n
p += 1
return p
maxp = maxd = 0
for d in range(1, 1000):
p = decimal_period(d)
if p > maxp:
(maxp, maxd) = (p, d)
print(maxd)
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