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p21-30.py
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p21-30.py
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from math import *
from time import time
def p23():
lim, sum_of = 28123, 0
ab_dict = [False] * lim
for i in range(lim):
dev_sum = 0
for d in range(1, int(sqrt(i)) + 1):
if i % d == 0:
dev_sum += d if d * d == i else d + i // d
ab_dict[i] = dev_sum - i > i
for i in range(1, lim):
add = True
for j in range(1, i):
if ab_dict[j] and ab_dict[i - j]:
add = False
break
if add:
sum_of += i
return sum_of
def p24():
per, digits = 1000000 - 1, 10
dig_list = list(range(digits))
fact = [1] + [i for i in range(1, digits)]
for i in range(1, digits):
fact[i] *= fact[i - 1]
num = ''
for i in range(digits):
digit = dig_list[per // fact[digits - 1 - i]]
dig_list.remove(digit)
num += str(digit)
per %= fact[digits - 1 - i]
return num
# for p26
def dig_cyc(num, search_to):
i, n = 0, 1
nums = []
while i < search_to:
nums += [n % num]
n *= 10
for j in range(i):
if nums[i] == nums[j]:
return i - j
i += 1
return search_to
def p26():
search_to = 1000
max_d, max_i = 1, dig_cyc(1, search_to)
for d in range(2, search_to):
i = dig_cyc(d, search_to)
if i > max_i:
max_i, max_d = i, d
return max_d
def p28():
num, sum_of, val = 1001, 1, 1
for i in range(1, num, 2):
for j in range(4):
val += i + 1
sum_of += val
return sum_of
def p29():
start, end, distinct = 2, 100, 0
have_been = []
for i in range(start, end + 1):
if i not in have_been:
max_of = int(log(end, i))
power_range = [False] * (max_of * end + 1)
for pow_i in range(1, max_of + 1):
for power in range(start, end + 1):
power_range[pow_i * power] = True
have_been += [pow(i, pow_i)]
for place in range(1, max_of * end + 1):
distinct += power_range[place]
return distinct
def p30():
start_num, p, digits = 2, 5, 10
max_num, sum_of = int((p + 1) * pow(digits - 1, p)), 0
for i in range(start_num, max_num):
old_num, new_num = i, 0
while old_num:
new_num += pow(old_num % digits, p)
old_num //= digits
if new_num == i:
sum_of += i
return sum_of
def timed_run():
start = time()
print(p30())
print(f"{time() - start:0.2f}s")
if __name__ == '__main__':
timed_run()