def euler_65():
"""Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e."""
from eutil import nth, digits
def sequence():
num = []
t = 0
while True:
if t == 0:
num.append(1)
elif t == 1:
num.append(2)
else:
coef = t / 3 * 2 if t % 3 == 0 else 1
num.append(coef * num[t - 1] + num[t - 2])
yield num[-1]
t += 1
return sum(digits(nth(sequence(), 100)))
def euler_7():
"""Find the 10001st prime."""
from eutil import primes, nth
return nth(primes(), 10000)
def euler_24():
"""What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?"""
from itertools import permutations
from eutil import nth
return "".join(map(str, nth(permutations(range(10), 10), 999999)))
