lychrel numbers

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lychrel numbers

michel paul-2
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.

- Michel

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

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

- Dr. Christos Papadimitriou
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