open System
open Microsoft.FSharp.Collections
let rec f1 n =
   if n = 1 then 1
   else if n = 2 then 2
   else f1 (n - 1) * f1 (n - 2)
let rec fib n =
    if n = 0 then 0
    else if n = 1 then 1
    else fib(n-2) + fib(n-1)
let f2 (s:string) : char =
   s.ToUpper() |> Seq.countBy id |> Seq.maxBy snd |> fst
let makeSeq (b:float) : seq<float> =
    (b, 1.) |> Seq.unfold (fun (x, y) -> Some (x, (x-1./sqrt(y), y+1.)))
let f3(k:int, lst: seq<float>) : List<float> =
    lst |> Seq.filter(fun (x) -> x < 0.) |> Seq.take(k) |> Seq.toList
let f4 =
    seq { 1 .. 1000 } |> Seq.filter(fun (x) -> x % 3 = 0 && x % 5 = 0) |> Seq.toList
let rec gcd a b =
 match b with
 | _ when b = 0 -> a
 | _ -> gcd b (a % b)
let lcm a b =
    a * b / gcd a b
let f5 =
    Seq.reduce (lcm) [1..20]
let ispalindrom (s:string):bool =
  s  = (s  |>  (fun  x -> new string(x.ToCharArray() |> Array.rev)))
let f6 =
    seq { 1 .. 1000 } |> Seq.filter(fun (x) -> ispalindrom(x.ToString()) && ispalindrom(Convert.ToString(x, 2))) |> Seq.fold (+) 0
let generate n =
    let m = 1 <<< n
    { 0 .. m-1 } |> Seq.map(fun(x) ->
        let s_2 = Convert.ToString(x, 2)
        let s = String.replicate(n-s_2.Length) "0"
        s+s_2 |> Seq.map(fun(x) -> x='1') |> Seq.toList) |> Seq.toList
let rec istrue (lst : List<bool>) : bool =
    match lst with
     | _ when lst.Tail.Tail <> []  -> istrue(lst.Tail) && (not(lst.Head && lst.Tail.Head) || (lst.Tail.Tail.Head))
     | _ when lst.Tail.Tail = [] -> true
let f10 (lst : List<List<bool>>) : int =
    let rec loop lst acc =
        match lst with
        | head::tail -> loop tail acc + Convert.ToInt32(istrue(head));
        | [] -> acc
    loop lst 0
//y_n = y_(n-1) + fib(n+1)
let rec f10_fib (n : int) : int =
    match n with
    | 2 -> 4
    | n -> f10_fib(n-1) + fib(n+1)
let rec extractDigits acc input =
    if input <= 9 then input::acc
    else extractDigits (input % 10::acc) (input/10)

let sumOfSquares input =
    input
    |> List.fold(fun acc i -> acc + i*i) 0
let sumOfSqr input =
    input
    |> List.fold(fun acc i -> acc + i) 0
let rec sum85 input =
    if input = 85 then true
    else if input = 1 || input = 4 then false
    else
        let newInput =
            input
            |> extractDigits List.empty
            |> sumOfSquares
        sum85 newInput
let makeArithmeticSeq a_1 d =
    a_1 |> Seq.unfold (fun x -> Some (x, x+d))
let get_a_n (sq:seq<int>, n:int)
    a_n = Seq.take(1)
let f7 (a_1:int, d:int, n:int) : int =
    a_1 |> Seq.unfold (fun x -> Some (x, x+d)) |> Seq.take(n) |> Seq.sum
let rec f8 input =
    if input >= 0 && input < 10 then input
    else let newInput =
            input
            |> extractDigits List.empty
            |> sumOfSqr
         f8 newInput
let f9 =
    seq {10..99} |> Seq.filter(fun (x) -> sum85 (x)) |> Seq.min
[<EntryPoint>]
let main argv =
    Console.WriteLine(f1(6))
    let list3 = f3(3, makeSeq(4.))
    printf "%A" list3
    Console.WriteLine()
    Console.WriteLine(f2("AAAAABbbbbbCC"))
    let list4 = f4
    printf "%A" list4
    Console.WriteLine()
    Console.WriteLine(f5)
    Console.WriteLine(f6)
    let list7 = generate 3
    printf "%A" list7
    Console.WriteLine()
    let n = 13
    Console.WriteLine(f10_fib(n))
    Console.WriteLine(f10(generate n))
    (*
    [10..99]
    |> List.filter(fun i -> sum85 i)
    |> List.iter(fun i -> printfn "%d" i)
    *)
    (*
    let ap = 2 |> Seq.unfold (fun x -> Some (x, x+3)) |> Seq.take(10) |> Seq.toList
    printf "%A" ap
    *)
    Console.WriteLine(f7 (2, 3, 5))
    Console.WriteLine(f8 65536)
    Console.WriteLine(f9)
    Console.ReadKey()
    0