The Magic of numbers - Number palindromes.

We can usually get a palindrome by reversing the digits of a number then adding it to the original number, then continuing the process till the palindrome is reached.

for example
87 + 78 = 165 ; 165 + 651 = 816 ; 816 + 618 = 1434 ; 1434 + 4341 = 5775. this took 5 steps.

The curious thing is we haven't been able to achieve a palindrome with the number 196 yet. The process has been taken to a number with 80,000 digits without success. No one knows if every 2 digit number and above will give a palindrome using this process.

Question

The Magic of numbers  -  Number palindromes.

We can usually get a palindrome by reversing the digits of a number then adding it to the original number, then continuing the process till the palindrome is reached.

for example 
87 + 78 = 165 ; 165 + 651 = 816 ; 816 + 618 = 1434 ; 1434 + 4341 = 5775.   this took 5 steps.

The curious thing is we haven't been able to achieve a palindrome with the number 196 yet. The process has been taken to a number with 80,000 digits  without success. No one knows if every 2 digit number and above will give a palindrome  using this process.

mathmate · Answer

.

ganeshie8 · Answer

Looks like one of the many interesting mysteries of numbers...

welshfella · Answer

I wonder why the process did not go further than 80,000 digits - Were they limited by the  power of the computers?

welshfella · Answer

Not sure when this article was published.  
Yes  numbers never cease to amaze.

welshfella · Answer

Also in this article it mentioned a math formula which is embedded in a C program that can tell you the value of any digit in pi. However pi must be written in hexadecimal!  Not of much practical use ......

ganeshie8 · Answer

Yeah I cannot think of any other reason. A number 80,000 digits is a huge unthinkable number !

ganeshie8 · Answer

is it even possible to imagine how big 10^80000  actually is ?

ganeshie8 · Answer

If it is online, could you share the article. I'd like to read...

welshfella · Answer

yes  - I looked at it the other day. 
I'll look for it now.

ganeshie8 · Answer

Okay, no hurry... post when ever you can... thanks :)

welshfella · Answer

OK

mathmate · Answer

Interesting phenomenon! The following link is probably more recent: http://www.magic-squares.net/palindromes.htm `By Sept. 11, 2003, Wade VanLandingham (Florida, U.S.A.) had tested the number 196 to 278,837,830 iterations, resulting in a number of 117,905,317 digits. It was still not a palindrome! ` Also, it appears that other numbers have the same property (of not producing palindromes): `The first few numbers of this chain are 196, 887, 1675, 7436, 13783. ` from the same source.

welshfella · Answer

Thanks @mathmate

The article I referred to was in 1998

mathmate · Answer

@welshfella 
If you have the original link, it would be still interesting to read, as  you mentioned there are other fascinating stuff in there, namely pi digits.  I read about it some time before, but have lost track of it.

welshfella · Answer

here's the link http://www.cs.man.ac.uk/~toby/writing/PCadvisor/numbers.htm

mathmate · Answer

@welshfella 
Thank you! :)