def is_lychrel_number(number: int, iteration_stop: int) -> bool:
"""Returns true if number is a Lychrel number
There are no numbers proven to be Lychrel. This process will use
iteration limited by the iteration_stop value.
"""
test_number = number
for _ in range(iteration_stop):
test_number = test_number + int(str(test_number)[::-1])
if is_palindrome(str(test_number)):
return False
return True
def p36(stop: int) -> int:
# Rather than test every number we'll build the palindrome
# numbers in base 10. We'll need the first half of the digits in
# the maximum value. If the length of the max is odd then we need
# to collect the middle digit as well.
# Cases: max value -> first half
# Case 1: 1 -> 1
# Case 2: 12 -> 1
# Case 3: 123 -> 12
# Case 4: 1234 -> 12 etc.
max_n = stop - 1
max_n_str = str(max_n)
max_n_len = len(max_n_str)
first_half_max_n_digits_len = max_n_len // 2 + max_n_len % 2
first_half_max_n_digits = max_n_str[:first_half_max_n_digits_len]
palindromes = [n for n in range(1, min(10, stop))]
# generate list of candidate palindromes
for generating_digits in range(0, int(first_half_max_n_digits) + 1):
generating_digits_str = str(generating_digits)
# determine left and right most digits
left_digits = generating_digits_str
right_digits = left_digits[::-1]
# even length palindromes (len: 2x)
even_palindrome = int(left_digits + right_digits)
if even_palindrome >= stop: break
palindromes.append(even_palindrome)
# odd length palindromes (len: 2x + 1)
for middle_digit in range(0, 10):
odd_palindrome = int(left_digits + str(middle_digit) +
right_digits)
if odd_palindrome >= stop: break
palindromes.append(odd_palindrome)
# now sum those that are also palindromes in base 2
return sum(n for n in palindromes if is_palindrome(bin(n)[2:]))
def test_1001001001(self):
self.assertEqual(is_palindrome('1001001001'), True)
def test_585(self):
self.assertEqual(is_palindrome('585'), True)
def test_10(self):
self.assertEqual(is_palindrome('10'), False)