055-LychrelNumbers.py

#!/usr/bin/python3
# -*- coding: utf-8 -*-
# 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?

def ispalindrome(n):
    if(str(n)==str(n)[::-1]):
        return(1)
    else:
        return(0)

lychrel = 0
for m in range(1,10000):
    n = m
    for i in range(50):
        if(ispalindrome(n+int(str(n)[::-1]))==1):
            break
        else:
            n += int(str(n)[::-1])
    else:
        lychrel += 1
print(lychrel)