Conference rusure::math

945.0. "A palindrome algorithm" by TLE::PETERSON (Bob) Thu Oct 13 1988 14:21

This may be of interest to the regular readers here.  A coworker's daughter
came home with this 4th grade arithmetic problem.

A number is a palindrome if its (base 10) representation is the same when
reversed.  Many numbers can be turned into palindromes by this algorithm:
	add the number to its reversed representation
e.g:
	 123
	+321
	====
	 444
Thus 123 turns into a palindrome after one iteration.

Can you tell if a number will become a palindrome if the above algorithm is
applied enough times?  For example, 196 will not turn into a palindrome after
3,500 iteration.  Interestingly most numbers (under 2,000) will result in
palindromes in 25 or so iterations.  

Already this has absorbed enough developers' time, so we turn it loose on you.
A program to perform these calculations in variable-precision arithmetic is
available in TLE::FORD2$:[PETERSON.PUBLIC]PAL.FOR.  Any intensive work should
perhaps be run on a low-use machine.

(Already we've found a property of we call family trees in the numbers which do
not become palindromes, aka `magic' numbers to us.  We have not been able to
predict these arbitrarily.)

     See note 525 and its replies.
     
     Dan

Arg!  Well, if people used standard english I would have found that note when I
searched for DIRECTORY/TITLE=PALINDROME.  I suppose I should have anticipated
this.

     You have to play it by ear.  Sometimes leaving off trailing
     letters (that would be chopped off by a suffix) when doing
     a search helps, but other times it results in finding
     too much.
     
     Dan