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I've been googling around a little lately and have stumbled across the so called Lychrel problem. For a natural number $x$, let $Rx$ denote the number obtained by reversing the base-$10$ digits of $x$ (i.e. $R90 = 9$, $R345 = 543$, etc.). Then the question is whether, given some initial $x$, the sequence defined by $x_{n + 1} = x_n + Rx_n \quad \quad \quad x_0 = x$ eventually produces a palindrome (i.e. $Rx_n = x_n$ for some $n$). An initial value for which no palindrome is ever obtained is called a Lychrel number. It is an open question whether any Lychrel numbers exist at all. The smallest suspected Lychrel number is $x = 196$. I've been trying to find out whether anyone has ever done any serious mathematical work on the issue, but all I have been able to find are either computational efforts or trivial facts. Does anyone know of any serious publications about this question?

Thanks in advance.

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    I have found this: http://homepages.thm.de/~hg10975/Lychrel.htm which looks somewhat more extensive than usual. I have yet to read it carefully though.2011-12-31

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There doesn't seem to be much ... But here are two interesting things i found in a quick search:

On Palindromes and Palindromic Primes Hyman Gabai and Daniel Coogan Mathematics Magazine Vol. 42, No. 5 (Nov., 1969), pp. 252-254  (article consists of 3 pages) Published by: Mathematical Association of  

Stable URL: http://www.jstor.org/stable/2688705

And

Numerical palindromes and the 196 Problem: http://www.osaka-ue.ac.jp/zemi/nishiyama/math2010/196.pdf

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    i searched a number of math journals looking for this stuff in addition to scholar.google.com i've put an alert out on a few subscriptions that i have, if get anything i'll post it for ya2011-12-28