Any serious work on Lychrel numbers/$196$-Algorithm? 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.
 A: 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
A: Short answer: Yes! That I'm aware of, no one has published any proof or even an article trying to solve the problem itself. However there are many recent (well at least post 2011) that deal with other aspects and side conjectures and related theorems.
I'm trying to bring this discussion back and thought of updating some of the most relevant and recent references:
Definitions

*

*Wikipedia definition of Palindromic Number: https://en.wikipedia.org/wiki/Palindromic_number

*Lychrel number: https://en.wikipedia.org/wiki/Lychrel_number

*Problem statement on Project Euler website: https://projecteuler.net/problem=55

*Reverse and add (or Reverse and sum) algorithm: https://mathworld.wolfram.com/196-Algorithm.html
"Classic" references to the problem or related

*

*Trigg, Charles W. "Palindromes by Addition." Mathematics Magazine 40, no. 1 (1967): 26-28. Accessed September 4, 2021. doi:10.2307/2689178.

NOTE: As far as I found in my research, Trigg's 1967 article above is the first reference of the Palindromic Conjecture in a scientific publication.

*

*Brousseau, Alfred. "Palindromes by Addition in Base Two." Mathematics Magazine 42, no. 5 (1969): 254-56. Accessed September 4, 2021. doi:10.2307/2688706.

*Trigg, Charles W. "More on Palindromes by Reversal-Addition." Mathematics Magazine 45, no. 4 (1972): 184-86. Accessed September 4, 2021. doi:10.2307/2688651.

*Gardner, M. Mathematical Circus: More Puzzles, Games, Paradoxes and Other Mathematical Entertainments from Scientific American. New York: Knopf, pp. 242-245, 1979.

*Gruenberger, F. "How to Handle Numbers with Thousands of Digits, and Why One Might Want To." Sci. Amer. 250, 19-26, Apr. 1984.

A: "Recent" references to the problem or related
Recently, Marius Coman, Romanian mathematician has publisehd a serie of related articles:

*

*Coman, M.. “Conjecture that there is no a Poulet Number to be as Well Lychrel Number.” viXra (2017): n. pag. http://vixra.org/pdf/1712.0554v1.pdf

*Coman, M.. “Number P^2-Q^2 Where P and Q Primes Needs Very Few Iterations of “reverse and Add” to Reach a Palindrome.” viXra (2018): https://vixra.org/pdf/1801.0082v1.pdf

*Coman, M.. “Conjecture that there is no a Square of an Odd Number to be as Well Lychrel Number.” viXra (2017): n. pag. - https://vixra.org/pdf/1712.0554v1.pdf
Other Authors

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*Mohamed Sghiar. BRISURE DE SYMETRIE ET NOMBRES DE LYCHREL. 2017. ´  (https://hal.archives-ouvertes.fr/hal-01433370)

*Markus Sigg, "On a conjecture of John Hoffman regarding sums of palindromic numbers", arXiv:1510.07507 https://arxiv.org/abs/1510.07507v1

*Gao, Y - Represent a natural number as the sum of palindromes in various bases

