lychrel numbers

[michel paul]

A couple of years ago I discovered lychrel numbers. 

Interesting. No one knows if they exist in base 10. 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 example of a kind of mathematics that just can't be effectively done with either pencil and paper or calculator. You really do need to program it. What tools do we need?  

• 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.
• If we haven't found a palindrome after a gazillion iterations, we need to stop.

It was a great activity. I used it as a project in my computational class. They had to create a set of functions that would find the lychrel number candidates in a given interval, and I was really pleased to see what some of the kids started to do. After creating the necessary functions 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.

I didn't do this last year, but I recently got reminded of this, and I'm going to do it again pretty soon here. I think this is a good example of what one would mean by 'computational' mathematics.

- 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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