module _46

let smallestOddCompositeNotSumOfPrimeTwiceSquare =
    let ceiling = 10000

    let composites =
        common.compositeArray ceiling
        |> Seq.filter (fun c -> c % 2 = 1)
        |> Set.ofSeq

    let twiceSquares =
        Seq.unfold (fun state -> Some(2 * state * state, state + 1)) 1

    let primes = common.primeArray ceiling
    let twiceSquareList = twiceSquares |> Seq.take ceiling
    
    let sumOfPrimceTwiceSquare =
        common.crossMap (+) primes twiceSquareList
        |> Seq.distinct
        |> Set.ofSeq

    Set.difference composites sumOfPrimceTwiceSquare