Lychrel Numbers
If we take $47$, reverse and add, $47 + 74 = 121$, which is palindromic.
Not all numbers produce palindromes so quickly. For example,
\begin{align} 349 + 943 &= 1292\\ 1292 + 2921 &= 4213\\ 4213 + 3124 &= 7337 \end{align}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.