[Edu-sig] lychrel numbers

[michel paul]

I just discovered lychrel
numbers<http://en.wikipedia.org/wiki/Lychrel_number>.
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<http://en.wikipedia.org/wiki/6174_%28number%29>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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