Welcome to p196.org!
I have had people ask me why I don't stop using a "Brute Force" method, and actually try to solve the 196 problem mathematically, with a bit of logic...
The same answer that I have given on the FAQ, I'll give here...
If I knew how... I would!!!
As a result, there is not that much in these pages about a mathematical approach to solve the question of whether any number is in fact a Lychrel Number!! I'm going to try to use this page to help that point. I guess it is my hope that someone will understand the following papers well enough, that they will be able to come up with a proof that will force me to stop searching.
Most of the following is a bit over my head. When I really stop and study the papers, I can just begin to understand what is going on, but I tend to forget it almost as fast as I read it. I hope that by forcing myself to keep up, I will begin to understand it all more completely!!
For right now, I have simply compiled other papers that I have found into one location. There is only a little work here that is my own. I am going to give the links for the papers, from where I find them on the internet, but I am also going to provide a "local copy" of the papers I list. Hyperlinks are forever changing and web pages are always disappearing. I think most of this information should be kept in some place, where it should still be accessible, even if the original site goes away.
If any of these papers are yours and you do not want them posted here, let me know and I promise, I will immediately remove them!!
But I hope that no one will mind my copying their work to share with others!!
For the local copies, I have changed the formatting on some of these, but I have not altered any of the spelling, words, or meaning of any of the papers. I have added a first line, which shows the original location of the file, but with the exception of hyperlinks, everything after the origin line, is from the original page. (You will have to use your back button to get back to this page.) I tried to get all the hyperlinks that were in the original paper to point to the correct pages, that they started from. Again, this was all "formatting", but I am trying to be completely frank about what I have, and haven't done. I have not tried to sort it all out in any order. Sorry if it is a mess, but......So....... Here goes.......
Here is a paper titled "Self-Similar Reverse-Sum Sequences" written by Kevin Brown, which Vincent Prosper says is of "particular interest". Locally it is HERE. One of the things that I found interesting about the number in his example: 17509097067. I ran it out a million iterations, and it did not form a palindrome, but it is not on the Lychrel list. It obviously comes from one of the threads. I'm still trying to figure out which Lychrel number it comes from....
Important comments taken from an email dated 1/19/03 from Vincent to Wade are only found locally, and are HERE.
Vincent Prosper and Sebastien Veigneau have a joint paper in Post Script format here or a local copy in PDF format here. It is a bit complex, and I don't see anything very different from what we've already identified and have been doing in our software coding, but it is good to read, none the less.
A few months ago I wrote the following notes to myself... I haven't finished any thoughts on it, and it's not complete, but maybe it'll give some new ideas to someone... (myself included!!!)
Back on 6/7/03, I had these notes on the blackboard.
On September 14, 2003 Vaughn Suite sent me the following.
On September 23, 2003 Vaughn added this short piece. As a note, at my request, Vaughn has modified his original app, to only save the first and last few digits of the iterations. For example, it will save the first and last 2 digits of every iteration, into a single text file. This has allowed both of us to play around with thousands or millions of iterations, without saving the entire iteration to a file. You can only imagine how much hard drive space this has saved me!!! My thanks to Vaughn for a copy of this app!!!
On November 5, 2003, Felipe Barone pointed out some articles from a discussion on a programming language called Icon. There are HERE originally, and the articles of interest are 30 through 35, 37, 39, 40, 43, 45 through 51, and 57. Even though it is aimed at applications written in Icon, it is well worth the time to read the articles, since they provide an array of ideas for math solutions to the questions about Lychrel numbers.
On April 29th, 2005, Chris Pazsint sent this paper with very clean description of how to UNDO the reverse and Add process. It was an inspirational read for me the first time I saw it. And if someone as simple as me can follow it, I'm sure the rest of you will have no problems!! :-) It is in MS Word format, so I hope everyone can view it. He sent a follow-up paper that is available HERE for those interested in reading it as well. Between the two, there are some great explanations on this well thought out idea. great job Chris!!!
In December of 2011, Jake Harry sent the following paper to me: A New Method of Generating Palindromes . It is a fresh look at an old problem.
Anyone want to comment about anything on this page???