-- It is possible to show that the square root of two can be expressed as an infinite continued fraction.
--
-- √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...
--
-- In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?
import Euler
import Data.Ratio

nDigits 0 = 0
nDigits n = 1 + nDigits (n `div` 10)

iterations = iterate (\x -> 1+1/(1+x)) (3%2)

main = print $ length $ filter (\x -> nDigits (numerator x) > nDigits (denominator x)) $ take 1000 iterations