F#: Project Euler 1 to 11

projectEuler1_11.fs

module ProjectEulerSolutions

open System
open System.Collections.Generic
open System.IO
open System.Linq

open ProjectEulerLib

let problem1 = [1..999] |> List.filter(fun x->x%3=0 || x%5=0) |> List.sum
let problem2 = Seq.unfold(fun(a,b)->Some(a,(b,a+b))) (1,2) |> Seq.takeWhile((>=)4000000) |> Seq.filter(fun n->n%2=0) |> Seq.sum
let problem3 = factorize 600851475143L |> List.rev |> List.head |> fst
let problem4 = [ for i in 100..999 do for j in i..999 -> i*j ].Where(fun x -> x=reverseDigit x).Max()
let problem5 = [1..20] |> Seq.collect factorize32 |> Seq.groupBy fst |> Seq.map(snd>>Seq.maxBy snd) |> Seq.fold(fun acc (p,n)->acc * pown p n)1
let problem6 =let ns = [1..100] in pown(List.sum ns)2 - (List.map(fun x->x*x) ns |> List.sum)
let problem7 = primes() |> Seq.skip 10000
let problem8 = problem8str.Where(Char.IsDigit).Select(string>>Int32.Parse) |> Seq.windowed 5 |> Seq.map(Seq.reduce( * )) |> Seq.max
let problem9 = [for a in 1..333 do for b in a..499 do let c=1000-a-b in if a*a+b*b=c*c then yield a*b*c]
let problem10 = primes() |> Seq.takeWhile((>)2000000) |> Seq.fold(fun acc x->int64 x+acc)0L