Считалочка до 5 на F#

// Author: Xelez

let removeAt index input =
  input
  |> List.mapi (fun i el -> (i <> index, el))
  |> List.filter fst |> List.map snd

let rec solve = function
| ([x], index) -> x
| (list, index) ->
    let k = (index + 4) % (List.length list)
    let newlist = list |> (removeAt k)
    solve (newlist, k)

let main input =
    solve (input, 0)

let rec calc_k = function
| 1 -> 1
| n ->
    let rec_k = calc_k (n-1)
    1 + (rec_k + 5 - 1) % n


let checker input =
    let k = input |> List.length |> calc_k
    List.nth input (k-1)