stubborn 196

[Deleted member 4993]

Write down any natural number, reverse its digits to form a new number, and add the two:
871
178
------
1049


In most cases, repeating this procedure eventually yields a palindrome:

1049
9401
-------
10450

10450
05401
--------
15851

With 196, perversely, it does not — or, at least, it hasn’t in computer trials, which have repeated the process until it produced numbers 300 million digits long.

Is 196 somehow immune to producing palindromes? No one’s yet offered a conclusive proof — so we don’t know
reference:
http://www.futilitycloset.com/2010/03/07/stubborn/

 

[soroban]

Hello, Subhotosh!

Write down any natural number, reverse its digits to form a new number, and add the two:

\(\displaystyle \begin{array}{cccc} &8&7&1 \\ +&1&7&8\\ \hline 1&0&4&9 \end{array}\)


In most cases, repeating this procedure eventually yields a palindrome:

\(\displaystyle \begin{array}{ccccc}&1&0&4&9 \\ +&9&4&0&1 \\ \hline 1&0&4&5&0 \end{array}\)


\(\displaystyle \begin{array}{cccccc}&1&0&4&5&0 \\ +&0&5&4&0&1 \\ \hline &1&5&8&5&1 \end{array}\)


With 196, perversely, it does not — or, at least, it hasn’t in computer trials,
. . which have repeated the process until it produced numbers 300 million digits long.

Is 196 somehow immune to producing palindromes?
No one’s yet offered a conclusive proof — so we don’t know

Reference: http://www.futilitycloset.com/2010/03/07/stubborn/

I first heard of this problem in the 1980's.
I wrote a BASIC problem on my Tandy1000 (remember those?)
. . and cranked it out to 500 iterations before giving up.

A quick search told me that 196 is a Lychrel number.
. . Some others seem to be: .\(\displaystyle 879,\;1997,\;7059\)

As you pointed out, 196 has been taken to 300 million digits with no palindrome.
. . (It was completed by Wade VanLandingham on May 1, 2006.)

 

[Denis]

As you pointed out, 196 has been taken to 300 million digits with no palindrome.
(It was completed by Wade VanLandingham on May 1, 2006.)

Reminds me of the guy who spent years sticking together over a million matches
forming a replica of London Bridge; admired for his tenacity, but could only get
5 bucks for it at the corner pawn shop :shock: