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Project Euler #65: Convergents of e

  • urossevkusic
     + 0 comments

    Python 3 solution, using the fact that the continued fraction of e has a pattern of 2 1 1 4 1 1 6 11, ..., from index 2:

    N = int(input())

from math import e

n0, n1 = 1, 2
t = 1

for i in range(1, N):
    n0, n1 = n1, n0 + t*n1
    t = 1 if (i - 1) % 3 != 0 else ((i - 1) // 3 + 1) * 2
    
print(sum(map(int, str(n1))))