Problem 55 : Lychrel numbers

Problem Statement

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?

Solution

def palin(n):
    return str(n) == str(n)[::-1]
lychrel = []
for num in range(10,10001):
    iteration = 1
    st_num = str(num)
    temp = int(st_num[::-1]) + num
    if palin(temp):
            continue
    else:
        while iteration<=50:
            temp1=str(temp)
            temp2=temp1[::-1]
            temp3 = int(temp1)+int(temp2)
            if palin(temp3):
                break
            else:
                temp = temp3
                iteration = iteration+1
        if iteration >50:
            lychrel.append(temp3)


print(len(lychrel))

Output

249