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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.
let naturalNumbers = Seq.unfold (fun state -> Some(state, state+1)) 1 let rec cycleLength n = if n % 2I = 0I then cycleLength (n/2I) else if n % 5I = 0I then cycleLength (n/5I) else naturalNumbers |> Seq.filter (fun x -> ((pown 10I x) - 1I) % n = 0I) |> Seq.head let answer = [1I..999I] |> Seq.maxBy cycleLength
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