def main():
lst = []
for i in range(2, 500):
for j in range(2, 50):
num = i**j
if euler.digit_sum(num) == i:
lst.append(num)
lst.sort()
return lst[LIMIT - 1]
def sqrt_digit_sum(n):
sqrt = int(n**0.5)
while len(str(sqrt)) < 100:
n *= 100
sqrt *= 10
while sqrt**2 < n:
sqrt += 1
sqrt -= 1
return euler.digit_sum(sqrt)
def main():
nom1, denom1 = 3, 1
nom2, denom2 = 8, 3
i = 3
step = 4
while True:
for _ in range(2):
nom1, denom1, nom2, denom2 = (
nom2, denom2, nom1 + nom2, denom1 + denom2
)
i += 1
if i == N:
return euler.digit_sum(nom2)
nom1, denom1, nom2, denom2 = (
nom2, denom2, nom1 + nom2 * step, denom1 + denom2 * step
)
step += 2
i += 1
if i == N:
return euler.digit_sum(nom2)
def main():
lst = [0 for _ in range(TEN)]
for i in range(1, 10):
lst[i] = 1
sums = [euler.digit_sum(a) for a in range(TEN)]
for _ in range(LIMIT - 1):
new_lst = [0 for _ in range(TEN)]
for i in range(TEN):
s = sums[i]
n = (i % TEN1) * 10
for j in range(SUM + 1 - s + i // TEN1):
new_lst[n + j] += lst[i]
lst = new_lst
return sum(lst)
def main():
return max(
euler.digit_sum(a**b) for a in range(1, 100) for b in range(1, 100))
def max_digit_sum(a, b):
"""Input: Two natural numbers a and b.
Output: The maximum digit sum of any number a ** b for
a and b less than the inputs."""
return max([digit_sum(i**j) for i in range(1, a) for j in range(1, b)])
def max_digit_sum(a, b):
"""Input: Two natural numbers a and b.
Output: The maximum digit sum of any number a ** b for
a and b less than the inputs."""
return max([digit_sum(i**j) for i in range(1, a) for j in range(1, b)])