Talk:Ducci sequence

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The common claim that Ducci iterations converge to a zero sequence iff the length of the sequence is a power of 2 is incorrect. The correct formulation is "Ducci iterations converge for any starting sequence iff the length of the sequence is a power of 2. For example, for N = 6, one gets to 0s starting with 101010, 123210, or 121210.

I recommend an external link

Alexb@cut-the-knot.com (talk) 04:38, 31 March 2008 (UTC)

Thanks for the feedback. I didn't quite understand the difference between the common claim and the correct formulation. Are you saying that there are sequences that converge but not to zeros? As your link states, it's possible to converge to e.g 333333 but this gives 000000 in the next step. EverGreg (talk) 10:40, 31 March 2008 (UTC)
No, what I am saying is that, even for N which is not a power of 2, there are sequences that converge to 0. The article says "It has been proven that for n not a power of two, the Ducci sequence will settle on a loop with 'binary' sequences. That is, with elements composed of only two different digits." This is incorrect. Again, for some starting sequences the iterations will converge to 0 even for, say, N = 6, as the three examples 101010, 123210, or 121210 show.


Alexb@cut-the-knot.com (talk) 22:39, 12 April 2008 (UTC)
Aha! yes 101010 do indeed converge to zeros. I've changed the text accordingly.EverGreg (talk) 14:22, 13 April 2008 (UTC)
Very good. Now please give credit where credit is due. An external link to the page suggested above will do the job. Besides a Java simulation, the page contains additional references including to a recent paper by Greg Brockman that brought him the 6th place at the Intel Science Talent Search Competition.
Alexb@cut-the-knot.com (talk) 03:10, 14 April 2008 (UTC)