I just discovered lychrel numbers. See http://www.p196.org/ Interesting. No one knows if they exist. There are candidates that have not produced palindromes despite massive computational investigation, but so far no proofs one way or the other.
This is a great class activity, similar to exploring the 6174 pattern that Kirby mentioned a few years ago. How would we go about finding such things? What tools do we need? Well, let's see - we need to be able to reverse the digits of a number, we need to be able to test a number to see if it's a palindrome, we need a way to count the number of iterations required to produce a palindrome, etc.
I brought this up in my computational classes yesterday, and I was pleased to see what some of the kids started to do. A couple of them started looking for patterns between the lychrel candidates, noting their distances from each other and noting that if n is a candidate then obviously reverse(n) is as well. And one kid pointed out that this is not a property of the numbers themselves but of the base 10 representations of the numbers as lists of digits. So in binary, we'd get a different set of lychrel candidates.
================================== "What I cannot create, I do not understand."
- Richard Feynman
================================== "Computer science is the new mathematics."
- Dr. Christos Papadimitriou ==================================