# Project Euler #2 in F#

Project Euler Problem 2 asks for the sum of all even Fibonacci numbers below 4 million.

My first attempt at this problem using functional programming with F#. I would've liked to use some kind of take-while function to keep generating Fibonacci numbers until they fulfilled certain conditions, but alas I could not find such a thing in F#.

open System

let rec fib n = match n with
| 0 | 1 | 2 -> n
| _ -> fib (n - 1) + fib (n - 2)

let rec nOfFibTermsUpUntil x y = if fib (y + 1) < x then nOfFibTermsUpUntil x (y + 1) else y

[for n in 0..nOfFibTermsUpUntil 4000000 0 -> fib n]
|> List.filter (fun x -> x % 2 = 0)
|> List.sum
|> printf "The sum of Fibonacci terms up until 4,000,000 is: %d"


I discovered an (arguably) better way of doing this in F# using Seq.unfold and tuples. I'll post the solution below.

open System

(1,1) |> Seq.unfold (fun (a, b) -> Some(a + b, (b, a + b)))
|> Seq.takeWhile (fun x -> x <= 4000000)
|> Seq.sumBy (fun x -> if x % 2 = 0 then x else 0)
|> printf "The sum of Fibonacci terms up until 4,000,000 is: %d"

• Technically, you're supposed to takeWhile x < 4000000 (not x <= 4000000) — not that it matters, since 4000000 is not a Fibonacci number. Nov 2, 2014 at 8:00
• Yeah, I think using seq instead of list is the right way here: you can't have a potentially infinite list, but you can do that with seq. Nov 4, 2014 at 22:35

Your base case of fib(2) = 2 is incorrect. No variant of the Fibonacci Sequence starts with 0, 1, 2,…. You just happen to get the same answer because the problem only cares about the even-valued terms.

To take the terms under 4 million, use Seq.takeWhile.

• You're right, removing that base case will still yield the correct answer and a valid Fibonacci sequence. Nov 2, 2014 at 7:19

The explicit names for things here hopefully show more clearly how unbind works.

let fibonacciSeq =
let generator state =
let (cur, prev) = state
let next = cur + prev
let state' = (next, cur)
Some (cur, state')
let more =
(1, 0)
|> Seq.unfold generator
seq {
0
yield! more
}