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MathGroup Archive 2002

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Re: 196 algorithm, Most Delayed Palindromic Number

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35312] Re: 196 algorithm, Most Delayed Palindromic Number
  • From: JasonADoucette at hotmail.com (Jason Doucette)
  • Date: Mon, 8 Jul 2002 03:15:55 -0400 (EDT)
  • References: <afe4g3$gvg$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I wrote this message below to an email address, thinking the person
who posted the message
http://library.wolfram.com/mathgroup/archive/1999/Oct/msg00083.html
would get it.  I did not realize it would appear on this newsgoup.

Since it has, I will post a follow up to this with more information
for those who are interested.  Please see below the message...

"Jason Doucette" <JasonADoucette at hotmail.com> wrote in message news:<afe4g3$gvg$1 at smc.vnet.net>...
> Hi Hans,
> 
> Regarding your post here:
> http://library.wolfram.com/mathgroup/archive/1999/Oct/msg00083.html
> 
> You may be interested in my page:
> http://www.jasondoucette.com/worldrecords.html
> 
> The way to speed up the algorithm is to use a real compiler, and use an
> array to store individual digits.  There are methods for improvement beyond
> this, but this is the main thing you need to concentrate on.
> 
> I have personally taken the quest to 13 million digits, and have passed it
> on - the current record is over 30 million!
> 
> Jason Doucette
> -------------------------
> homepage: http://www.jasondoucette.com/
> e-mail: JasonADoucette at hotmail.com
> icq: 15860597

I thought it would be a good idea to give a current update of
these quests, and a short description of both for those who have never
heard about them.

196 Palindrome Quest:
---------------------

Most people have heard about the 196 Palindrome Quest (or the 196
Algorithm, as some people call it) via Reversal-Addition.  It arrives
from a process explained in a 1984 issue of Scientific American:

1. Pick a number.
2. Reverse its digits and add this value to the original number.
3. If this is not a palindrome, repeat the process.

It was conjectured that all numbers would eventually produce
palindromes this way, but 196 is the first number that does not appear
to do so.

I have personally taken the 196 Palindrome Quest to 13,000,000 digits:
http://www.jasondoucette.com/worldrecords.html

I have since passed on my record to Wade VanLandingham, and he has
continued the Quest to over 30,000,000 digits!
http://www.p196.org/

Most Delayed Palindromic Number:
--------------------------------

With the same process as above, most people have heard about the
strange case of number 89.  It takes 24 iterations to become a
palindrome:
http://www.jasondoucette.com/cgi-bin/pal.cgi?89

I hold the current world record for the number that takes the longest
number of steps to produce a palindrome.  It is a 15 digit number:
100,120,849,299,260
It takes 201 iterations to produce a 92 digit long number:
http://www.jasondoucette.com/cgi-bin/pal.cgi?100120849299260

I have solved numerous other numbers that solve in many more steps
than 24.  You can view these results on my website:
http://www.jasondoucette.com/worldrecords.html

Common Mistakes:
----------------

99% of the web pages on the Internet regarding the 196 Palindrome
Quest believe that 196 is the only number that does not solve out (or
the only number under 10,000 that does not solve out).  This is not
true.  Obviously, 691 (196 reversed), or 295 (the outer digits equal
the same sum: 1+6 = 2+5) both do not solve out either, because after
the first iteration of these numbers, they all result in the same sum
as 196 does after one iteration: 887 (and thus, 887 never solves out,
either, since it is the second step of the 196 sequence).  Find more
about Lychrel numbers (numbers that do not solve out via
reversal-addition) on Wade's pages:
http://www.p196.org/

Jason Doucette
http://www.jasondoucette.com/


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