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

[David Applegate]

Sorry about the attachment; I forgot that seqfan automatically purges
attachments.

I've placed the code at http://www.research.att.com/~david/oeis/seqparity.cc
I've placed the output at http://www.research.att.com/~david/oeis/seqparity.out

I concur with Hans's final term of (102853,99095).  There is a unique
choice at each step (other than swapping the even and odd counts) that
leads to this final term, because the sequence is unambiguous going
backwards: the total sequence has 102853 odd digits and 99095 even
digits.  If you drop the last term, you drop 8 odd digits and 5 even
digits, so the previous term must have 102853-8=102845 odd digits and
99095-5=99090 even digits, etc.

I've put the unique 17187-term sequence starting with 22 at
http://www.research.att.com/~david/oeis/seqparity.txt
Each line gives two versions of the term; the first puts the odd count
first, the second is the lesser of the two orders.  So, it starts

1 22 22
2 3132 3132
3 4162 4162
4 7172 7172
5 101102 101102
6 151112 112151
7 181142 142181
8 201182 182201
9 231212 212231
10 241262 241262
...

where the first place the two terms differ is for n=6.

-Dave