The Heavy Way to FizzBuzz solution

let fb nn =

    // set of all numbers
    let all =
        seq { for i in 1 .. nn do yield i }
        |> Set.ofSeq

    // an ideal of Z ring  (Z = field of integers)
    // http://en.wikipedia.org/wiki/Ideal_(ring_theory)
    let nZ n =
        seq { for i in 1 .. nn/n do yield i * n }
        |> Set.ofSeq

    // no buzz, no fizz...
    let onlynormal =
        nZ 3 |> Set.union (nZ 5)
        |> Set.difference all
        |> Set.map (fun x -> (x, x.ToString()))

    // only "fizzes"
    let buzzes =
        nZ 15 |> Set.difference (nZ 3) |> Set.map (fun x -> (x, "Fizz"))

    // only "buzzes"
    let fizzes =
        nZ 15 |> Set.difference (nZ 5) |> Set.map (fun x -> (x, "Buzz"))

    // only "fizzbuzz"
    let buzzfizzes =
        nZ 15 |> Set.map ( fun x -> (x, "FizzBuzz"))

    // result
    onlynormal
    |> Set.union buzzes
    |> Set.union fizzes
    |> Set.union buzzfizzes
    |> Set.toList
    |> List.map (fun x -> snd x)


// first 99
printfn "%A" (fb 99)

// 597 position
printfn "%s" (fb 600).[597-1]

// 1200 position
printfn "%s" (fb 1200).[1200-1]

// 9995 position
printfn "%s" (fb 10000).[9995-1]