Euler.fs

#light
open System.Numerics

(*

Problem #1
Answer: 234168

If we list all the natural numbers below 10 that are multiples of 3 or
5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

*)

let euler1 =
    [ for x in 1..999 do
      if x % 3 = 0 || x % 5 = 0
      then yield x ] |> List.fold (+) 0


(*

Problem #2
Answer:

Each new term in the Fibonacci sequence is generated by adding the
previous two terms. By starting with 1 and 2, the first 10 terms will
be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

Find the sum of all the even-valued terms in the sequence which do not
exceed four million.

*)

// let fibs =
//     Seq.unfold
//         (fun (current, next) -> Some(current, (next, current + next)))
//         (BigInteger 0, BigInteger 1)

// let fibs = Seq.initInfinite (fun n ->
//                              match n with
//                              | 0 -> 1
//                              | 1 -> 2
//                              | _ -> (fibs (n - 1)) + (fibs (n - 2)))


// let euler2 =
//     [ for x in Seq.take 39999999 fibs do
//       if x % (BigInteger 2) = (BigInteger 0)
//       then yield x ] |> List.fold (+) (BigInteger 0)

//let eulers = [ euler1; euler2 ]
let eulers = [ euler1; ]


let rec do_eulers xs =
    match xs with
    | [||] -> do_eulers [| 1 .. eulers.Length |]
    | _  -> for x in xs do
                let n = (string >> int) x
                printfn "%d. %d" n eulers.[n - 1]


[<EntryPoint>]
let main args =
    do_eulers (Array.map (string >> int) args)
    0