euler047.fsx

Jelmer047.fsx

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(* Project Euler Problem 47: Distinct primes factors

The first two consecutive numbers to have two distinct prime factors are:

14 = 2 × 7
15 = 3 × 5

The first three consecutive numbers to have three distinct prime factors
are:

644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.

Find the first four consecutive integers to have four distinct prime
factors. What is the first of these numbers? *)

let isprime n = (n=2) || not (List.exists (fun d -> n%d=0) ([2]@[3..2..(int(sqrt(float n)))]))

let primes = [|for n in 2..2999 do if (isprime n) then yield n|]

let pfs x = Array.length (Array.filter (fun d -> x%d=0) (Array.takeWhile (fun p -> p < x/2) primes))

let pfsxyz x = ((pfs (x) = 4) && (pfs (x+1) = 4) && (pfs (x+2) = 4) && (pfs (x+3) = 4))

let consecutives upto = [for n in 1..upto do if (pfsxyz n) then yield n]

printfn "%O" (consecutives 150000)

val isprime : n:int -> bool

Full name: Script.isprime

val n : int

val not : value:bool -> bool

Full name: Microsoft.FSharp.Core.Operators.not

Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
  | ( [] )
  | ( :: ) of Head: 'T * Tail: 'T list
  interface IEnumerable
  interface IEnumerable<'T>
  member Head : 'T
  member IsEmpty : bool
  member Item : index:int -> 'T with get
  member Length : int
  member Tail : 'T list
  static member Cons : head:'T * tail:'T list -> 'T list
  static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>

val exists : predicate:('T -> bool) -> list:'T list -> bool

Full name: Microsoft.FSharp.Collections.List.exists

val d : int

Multiple items
val int : value:'T -> int (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int

--------------------
type int = int32

Full name: Microsoft.FSharp.Core.int

--------------------
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

val sqrt : value:'T -> 'U (requires member Sqrt)

Full name: Microsoft.FSharp.Core.Operators.sqrt

Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>

val primes : int []

Full name: Script.primes

val pfs : x:int -> int

Full name: Script.pfs

val x : int

module Array

from Microsoft.FSharp.Collections

val length : array:'T [] -> int

Full name: Microsoft.FSharp.Collections.Array.length

val filter : predicate:('T -> bool) -> array:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.filter

val pfsxyz : x:int -> bool

Full name: Script.pfsxyz

val consecutives : upto:int -> int list

Full name: Script.consecutives

val upto : int

val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn

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More information

Link:	http://fssnip.net/sZ
Posted:	8 years ago
Author:	jelmer
Tags:	f# , fsharp , euler , tryfsharp