module _57

open common
open Fraction
open System
open System.Numerics

let sqrtTwoDigits =
    let sqrtTwoConvergent d =
        let rec sqrtTwo = function
            | 1 -> (2I,1I)
            | d -> addI (2I,1I) (reciprocalI(sqrtTwo (d - 1)))
        addI (1I,1I) (reciprocalI(sqrtTwo d))

    let digitCount n =
        let d = BigInteger.Log10(n)
        Math.Floor d + 1.0 |> int

    [1..1000]
    |> List.map sqrtTwoConvergent
    |> List.map (fun (n,d) -> (digitCount n, digitCount d))
    |> List.mapi (fun i (n,d) -> i + 1, n > d)
    |> List.filter (snd >> ((=) true))