If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
Not all numbers produce palindromes so quickly. For example,
349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337
That is, 349 took three iterations to arrive at a palindrome.
Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
How many Lychrel numbers are there below ten-thousand?
NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
def palindromes(number_str): result = True for i in range(0, len(number_str) / 2): if not number_str[i] == number_str[len(number_str) - 1 - i]: result = False break return result def rev(number): result = 0 while number >= 10: result += number % 10 result *= 10 number /= 10 result += number return result def process(number, level): result = number + rev(number) while not palindromes(str(result)): result += rev(result) level += 1 if level > 49: return result, False return result, level count = 0 for i in range(1, 10001): result, status = process(i, 1) # print i, process(i, 1) if status is False: count += 1 print count
while number >= 10:原来写成 while number > 10: 结果怎么都算不对