module _49

open common

let rec insertions x = function
    | []             -> [[x]]
    | (y :: ys) as l -> (x::l)::(List.map (fun x -> y::x) (insertions x ys))

let rec permutations = function
    | []      -> seq [[]]
    | x :: xs -> Seq.concat (Seq.map (insertions x) (permutations xs))

let primeSequence =

    let primes =
        primeArray 10000 |> Seq.skipWhile ((>) 999) |> Array.ofSeq
    
    let isPrime = isPrimeFunByArray primes

    primes
    |> Seq.map (
            numDigits >> List.ofArray >> 
            permutations >>
            Seq.map (Array.ofList >> digitsNum) >>
            Seq.filter isPrime >>
            Seq.distinct >>
            Seq.sort >>
            Seq.toArray
        )
    |> Seq.distinct
    |> Seq.collect (List.ofSeq >> combinations 3)
    |> Seq.filter (fun a -> a.[2] - a.[1] = a.[1] - a.[0])
    |> Seq.map (List.rev >> List.map (numDigits >> Array.map (string) >> Array.fold (+) "") >> List.fold (+) "")
    //|> Seq.toArray