def get_farey_series_length_recursive(d_1, d_2, d_max):
    if d_1 + d_2 > d_max:
        return 0
    d_med = d_1 + d_2
    l_min = get_farey_series_length_recursive(d_1, d_med, d_max)
    l_max = get_farey_series_length_recursive(d_med, d_2, d_max)
    return l_min + 1 + l_max


def get_farey_series_length(d_1, d_2, d_max):
    new_pairs = [(d_1, d_2)]
    s = 0

    while new_pairs:
        pairs = new_pairs
        new_pairs = []
        for d_1, d_2 in pairs:
            d_new = d_1 + d_2
            if d_new <= d_max:
                s += 1
                new_pairs.append((d_1, d_new))
                new_pairs.append((d_new, d_2))
    return s


def euler_073():
    d_max = 12000
    s = get_farey_series_length(2, 3, d_max)
    return s


if __name__ == "__main__":
    print("e073.py: " + str(euler_073()))
    assert(euler_073() == 7295372)