:tmp $ time ./collatz.native 1000000
    start: 837799 length 329

    real	0m0.782s
    user	0m0.776s
    sys	0m0.004s

    exception Error of string

    let (@@) f x  = f x
    let error fmt = Printf.kprintf (fun msg -> raise (Error msg)) fmt

    let max (a, x) (b, y) = if x > y then (a, x) else (b, y)

    let length start =
        let rec loop len a = 
            let next = if a mod 2 = 0 then a/2 else (3*a+1)/2 in 
            if a != 1 then
                loop (len+1) next
            else
                len
        in
            loop 0 start
                
    let collatz limit =
        let rec loop start longest =
            if start >= limit 
            then longest 
            else loop (start+1) (max longest (start, length start)) 
        in
            loop 1 (1,0)

    let report (start, len) = Printf.printf "start: %d length %d\n" start len

    let main () =
        let argv        = List.tl @@ Array.to_list Sys.argv in
        match argv with
        | []    -> report @@ collatz 10000
        | [n]   -> report @@ collatz @@ int_of_string n
        | _     -> error "usage: collatz [n]"

    let () = main ()