(* The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn1 + Fn2, where F1 = 1 and F2 = 1.

Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144

The 12th term, F12, is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits? *)

open Big_int;;

let rec fib x y n =
        if(String.length (string_of_big_int x) = 1000)
        then (Printf.printf "%d %s\n" n (string_of_big_int x))
        else fib (add_big_int x y) x (n+1)
in
        fib (big_int_of_int 1) (big_int_of_int 1) 2
;;