PROJECT EULER #57

Link to Project Euler problem 57

It is possible to show that the square root of two can be expressed as an infinite continued fraction.

Sqrt(2) = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...

By expanding this for the first four iterations, we get:

1 + 1/2 = 3/2 = 1.5
1 + 1/(2 + 1/2) = 7/5 = 1.4
1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...

The next three expansions are 99/70, 239/169, and 577/408, but the eighth expansion, 1393/985, is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.

In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?

using System;

namespace project_euler
{
class Program
{
    static void Main()
    {
        //Problem 57
        //(a+b)/b, where b = previous a+2*b and a = previous a + b.
        DateTime start = DateTime.Now;
        int count=0;
        BigInt a = new BigInt(3);
        BigInt b = new BigInt(2);
        for (int i = 1; i < 1000; i++)
        {
            if (a.ToString().Length > b.ToString().Length)
                count++;
            a = 2*b + a;
            b = a - b;
        }
        Console.WriteLine(count);
        TimeSpan time = DateTime.Now - start;
        Console.WriteLine("This took {0}", time);
        Console.ReadKey();
    }
}
}