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?

NOTE: Wording was modified slightly on \( 24 \) April \( 2007 \) to emphasise the theoretical nature of Lychrel numbers.