Problem 57 : Square root convergents

Problem Statement

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

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

The next three expansions are 9970, 239169 and 577408 but the eighth expansion, 1393985, 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 the denominator?

Solution

import math as mt

n=3
d=2
count =0

for i in range(2,1001):
    n,d = 2*d+n,n+d
    if int(mt.log10(n)) > int(mt.log10(d)): count += 1

print(count)

Output

153