project_euler.problem_057.sol1

Project Euler Problem 57: https://projecteuler.net/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 + …)))

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 the denominator?

Functions

solution(→ int)

returns number of fractions containing a numerator with more digits than

Module Contents

project_euler.problem_057.sol1.solution(n: int = 1000) → int

returns number of fractions containing a numerator with more digits than the denominator in the first n expansions. >>> solution(14) 2 >>> solution(100) 15 >>> solution(10000) 1508