The Most Delayed Palindromic Number and The 196 Palindrome Quest
Jason Doucette
I posted this message to some other newsgroups, and wanted it on these
ones, as well, since I think you guys would be interested. It didn't
seem to appear - perhaps the system thought I was spamming. I will
attempt once again:
Recently, one of my emails regarding these quests (in the message
title) got posted on a newsgroup (which I did not know would happen)
and 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/
Nis Jorgensen
Doucette) wrote:
>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/
>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).
Could you please post links to some of the at least 133 pages
(allowing for rounding) which make this error?
--
Nis Jorgensen
Amsterdam
Please include only relevant quotes, and reply below the quoted text. Thanks
Jason Doucette
> Doucette) wrote:
>
> >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).
Nis Jorgensen <n...@dkik.dk> wrote in message news:<osniiuodeua5a8l1u...@4ax.com>...
>
> Could you please post links to some of the at least 133 pages
> (allowing for rounding) which make this error?
Are you asking me to search and find at least 133 pages on the
Internet that state the error that 196 is the only number under 10,000
that does not resolve into a palindrome via the reversal-addition
process?
If you would like to see them, simply do a search on the web for "196
palindrome".
You will notice that most of the pages obviously quote other pages
without doing any other research, therefore they quote all of the
mistakes. More pages quote these pages, which has resulted in the
vast majority of them being incorrect.
I do not know which page start most of this mess, but it has left
people in awe that there is something majestic about 196 - however, it
is certainly not the case. In my recent discoveries, I have found
about 75% of all numbers 14 digits or less do not appear to ever solve
out. The larger the numbers get, the higher that percentage gets...
Only about 3% of all numbers 4 digits or less do not appear to ever
solve out.
Also, where did you get 133 from?
Jason Doucette
http://www.jasondoucette.com/
dhrm77
I assume that he meant that, allowing for rounding, the minimum number of
pages that would justify for the statement "99% of the web pages ..." is 66.
Assuming that 1 page in 67 doesn't make the mistake, then 66 out of 67 make
the mistake which turns out to be 98.507% or 99% (rounded to the nearest
whole percent)...
Somehow he doubled this number....
133 out of 134 turns out to be 99.25% which is nowhere near the maximum or
minimum limits for a rounded 99%...
D.
"Jason Doucette" <JasonAD...@hotmail.com> wrote in message
news:67828976.02070...@posting.google.com...
Michael Mendelsohn
> I think Nis Jorgensen made a small mistake when calculating 133.
> I assume that he meant that, allowing for rounding, the minimum number of
> pages that would justify for the statement "99% of the web pages ..." is 66.
> Assuming that 1 page in 67 doesn't make the mistake, then 66 out of 67 make
> the mistake which turns out to be 98.507% or 99% (rounded to the nearest
> whole percent)...
> Somehow he doubled this number....
If you look up the old posts in the thread (use the References: header
or google), you'll find that Jason Doucette gave *two* web pages that
presumably have it correct; and 133 out of 135 is 0,9851851851852 ,
though 132/134 would have done as well.
Have fun with percentages
Michael
--
When the tongue or the pen is let loose in a phrenzy of passion,
it is the man, and not the subject, that becomes exhausted.
-- Thomas Paine, "On Usenet"
Jason Doucette
> If you look up the old posts in the thread (use the References: header
> presumably have it correct; and 133 out of 135 is 0,9851851851852 ,
> though 132/134 would have done as well.
>
> Have fun with percentages
> Michael
When I stated "99%" I was approximating. I know the value is close to
99%, but I do not know what the exact value is.
Since the construction of my web page, I have educated many others who
already maintain palindrome web pages, as well as the owners of web
pages that have followed me, such as http://www.p196.org (which is now
continuing the 196 palindrome quest - although, the owner has educated
himself with regard to much of the material). Therefore, the
percentage of web pages with these errors have probably dropped, as
old web pages are modified to fix the errors, and new web pages are
based off of my page which contains no errors.
Jason Doucette
http://www.jasondoucette.com/