def concat_nums_2_length():
n_list = []
i = 1
while len(n_list) < 1000001:
n_list += digits_list(i)
i += 1
return map(str, n_list)
def cubic_perms(n_perms):
cubed_dict = {}
for i in count(100):
ccc = int_from_digits(sorted(digits_list(i**3), reverse=True))
if ccc in cubed_dict:
cubed_dict[ccc].append(i)
if len(cubed_dict[ccc]) > n_perms - 1:
# print(cubed_dict[ccc])
return cubed_dict[ccc][0]**3
else:
cubed_dict.setdefault(ccc, []).append(i)
def is_1_2_3_4_5_6_7_8_9_0(n):
digs = digits_list(n)
if len(digs) != 19:
return False
the_digs = [digs[index] for index in range(0, 19, 2)]
for i in range(10):
if i == 9 and the_digs[9] == 0:
return True
if i + 1 != the_digs[i]:
return False
return True
def is_bouncy(n):
digits = digits_list(n)
increasing = False
decreasing = False
for i in range(0, len(digits)-1):
if digits[i+1] < digits[i]:
increasing = True
elif digits[i+1] > digits[i]:
decreasing = True
if increasing and decreasing:
return True
return False
def p049():
four_dig_primes = [i for i in range(1000, 10000) if is_prime(i)]
num_4dig_primes = len(four_dig_primes)
prime_perms = defaultdict(list)
for prime in four_dig_primes:
sorted_digs = tuple(sorted(digits_list(prime)))
prime_perms[sorted_digs].append(prime)
topop = [k for k, v in prime_perms.items() if len(v) < 3]
for toop in topop:
prime_perms.pop(toop)
validsets = []
for k, v in prime_perms.items():
for combo in combinations(v, 3):
if combo[1] - combo[0] == combo[2] - combo[1]:
validsets.append(combo)
return int("".join(str(n) for n in validsets[1]))
def p020():
return sum(digits_list(factorial(100)))
def is_circ_prime(n):
digist = [int(j) for j in digits_list(n)]
return all((is_prime(int_from_digits(i)) for i in rotations_gen(digist)))
def is_digit_factorial(n):
return n == sum(map(factorial, digits_list(n)))
def digit_factorial(n):
return sum(digfact[i] for i in digits_list(n))
def p056():
return max(
(sum(digits_list(i**j)) for i in range(1, 100) for j in range(1, 100)))
def digit_powers(number, power):
return number == sum(map(lambda x: x**power, digits_list(number)))