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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Proof that 10110 is a Lychrel number''
by mathwizard on 2002-09-12 06:55:51 |
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| A friend of mine proved to me that this is indeed a Lychrel number, yet the proof is quite simple and short so that it doesn't make a complete entry, but if you want to include it here is how it goes:
10110->100011->1010100->1101001->10110100, which are not Palindromes. But 10110100 is of the form
10(n-times 1)01(n-times 0). Applying the transformation yields:
11(n-2 times 0)1000(n-2 times 1)01
and then
10(n times 1)01(n+1 times 0)
which becomes
11(n times 0)10(n-1 times 1)01
finally resulting in
10(n+1 times 1)01(n+1 times 0)
Which is again of the form discussed above. In this process we never get a Palindrome and thus 10110 is Lychrel.
--
"Do not meddle in the affairs of wizards for they are subtle and quick to anger." |
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