from e057 import add_fractions


def next_expansion(previous_numerator, previous_denumerator, value):
    if previous_numerator == 0:
        return (value, 1)
    return add_fractions(previous_denumerator, previous_numerator, value, 1)


def euler_065():
    e_sequence = [2] + [n for i in range(2, 1000, 2) for n in (1, i, 1)]
    n, d = 0, 1
    for i in range(100, 0, -1):
        n, d = next_expansion(n, d, e_sequence[i - 1])
    s = sum([int(l) for l in str(n)])
    return s


if __name__ == "__main__":
    print("e065.py: " + str(euler_065()))
    assert(euler_065() == 272)