projeul_pr55.py

"""Problem 55: Lychrel numbers

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?"""

c=0
for i in range(1,10000):
    strait=i+int(''.join(reversed(str(i))))
    reverse=int(''.join(reversed(str(strait))))
    d=1
    while d<50:
        if strait==reverse:
            break
        d+=1
        strait+=reverse
        reverse=int(''.join(reversed(str(strait))))
    else:
        c+=1

print(c)