[seqfan] Re: Look and say -- my parity

[M. F. Hasler]

Great work, Hans!
(And good idea to keep only the number of endpoints after n steps.
BTW, that count could/should be a sequence in OEIS !)

On Wed, Aug 20, 2014 at 5:05 PM, Frank Adams-Watters
<franktaw at netscape.net> wrote:
> That looks like a definite maybe to me. Interesting graph.

To me the graph looks growing...
(Are there bigger and smaller dots, or is this an "optical illusion"?)
Is there a simple explanation for the very regular pattern between 200
and 2000 and why it breaks down ?
(It looks as if it was exactly periodic between 500 and 2000.)

Maximilian

> -----Original Message-----
> From: Hans Havermann <gladhobo at teksavvy.com>
>
>> Jean-Marc Falcoz just computed this 62-term chain, telling me that
>
> this might
> be beaten.
>
> Without the "extend W with the smallest available integer" restriction,
> there's
> a chance of infinite chains. Start with '22'. Except I'm not going to look
> at
> the numerical representations, just the (odd,even) digit counts. So, start
> with
> (0,2):
>
> # 1   1:  (0,2).
> # 2   2:  (0,4), (3,3).
> # 3   3:  (0,6), (3,5), (4,6).
> # 4   4:  (0,8), (3,7), (4,8), (7,7).
> # 5   6:  (3,9), (3,10), (7,9), (7,10), (10,9), (10,10).
> # 6   6:  (6,11), (7,11), (10,12), (11,12), (14,11), (15,11).
> # 7   7:  (8,14), (10,13), (10,14), (15,13), (15,14), (18,13), (18,14).
> # 8   7:  (13,15), (14,15), (15,15), (18,16), (19,16), (20,18), (21,16).
> ...
> #62  16:  (213,205), (228,189), (229,188), (230,187), (231,186), (231,187),
> (232,185), (232,186), (233,184), (234,183), (234,184), (235,182), (235,183),
> (236,181)*, (236,182), (239,179).
>
> (236,181)* corresponds to Falcoz's final term 18122361 so I'm hopeful that
> I've
> set this up correctly and that my program works as expected. I'm not
> interested
> in chaining the counts across iterations, only in how many counts there are,
> because if that number drops to zero we are done and the chain is finite.
> Here's
> a graph of the counts:
>
> http://chesswanks.com/num/EvenOdd.png
>