lychrel numbers

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lychrel numbers

michel paul-2
I just discovered lychrel numbers.  See  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.

- Michel

"What I cannot create, I do not understand."

- Richard Feynman
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou

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