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

[David Applegate]

I've updated my c++ code at
http://www.research.att.com/~david/oeis/seqparity.cc
It now handles arbitrary bases, and handles zero counts more cleanly.

For digits in arbitrary bases, it uses 0-9, A-Z for values 10-35, and
<d> for values >= 36.

I also wrote a code to run a given pair backwards, at
http://www.research.att.com/~david/oeis/seqparityrev.cc

So, for example, "seqparityrev 102853 99095 10" (10 is the base, and
is the default) will generate the 17187 term sequence starting with
(102853,99095) and ending with (0,2)

Looking at various bases, the maximum ending point(s) are:

base 2 step 53 size 2 : (111111110,110011001) (111111111,110011000)
base 3 step 4 size 1 : (101,110)
base 4 step 637 size 1 : (1003312,333231)
base 5 step 56 size 1 : (1441,1404)
base 6 step 104 size 1 : (2134,1501)
base 7 step 1900 size 1 : (41022,45542)
base 8 step 6641 size 2 : (120430,113042) (120433,113037)
base 9 step 493 size 2 : (2813,3226) (2817,3222)
base 10 step 17187 size 1 : (102853,99095)
base 11 step 383 size 1 : (1133,11A5)
base 12 step 84 size 1 : (209,188)
base 13 step 618 size 1 : (1115,11C3)
base 14 step 1398 size 1 : (25D8,214D)
base 15 step 3940 size 1 : (57E9,589C)
base 16 step 1302 size 1 : (1639,13AD)
base 17 step 244 size 1 : (2GC,30C)
base 18 step 1586 size 2 : (11HA,1111) (11HB,1110)
base 19 step 11730 size 1 : (82GC,87CC)
base 20 step 32278 size 1 : (101JE,JE6C)
base 21 step 4146 size 1 : (221F,1HA7)
base 22 step 9376 size 2 : (46FG,3L0H) (46FH,3L0G)
base 23 step 58556 size 1 : (108AI,11CAI)
base 24 step 3974 size 1 : (14LH,133A)
base 25 step 1755 size 2 : (AJC,AML) (AJM,AMB)
base 26 step 29017 size 1 : (845L,7L1M)
base 27 step 6486 size 1 : (1C1L,18C1)
base 28 step 8983 size 1 : (1QDF,1H4O)
base 29 step 12027 size 1 : (29HO,21SB)
base 30 step 203794 size 1 : (1AI5G,179SP)
base 31 step 7585 size 2 : (100B,10EQ) (100D,10EP)
base 32 step 12491 size 1 : (1OTQ,1G5B)
base 33 step 7201 size 1 : (PPR,QDP)
base 34 step 10155 size 1 : (1199,10MU)
base 35 step 446199 size 1 : (1MQDS,1HHCL)
base 36 step 13506 size 1 : (185T,155G)
base 37 step 9067 size 1 : (PRX,QHX)
base 38 step 18710 size 1 : (1KFV,1D92)
base 39 step 104389 size 1 : (8I5X,8NVR)
base 40 step 16772 size 1 : (12J7,11G<36>)
base 41 step 1720 size 1 : (3<40>Z,3JD)
base 42 step 1605 size 1 : (3EP,38<38>)
base 43 step 82887 size 1 : (4<38>04,50<36><36>)
base 44 step 22153 size 1 : (12B<37>,11BS)
base 45 step 12410 size 1 : (N<41><39>,OH<37>)
base 46 step 35902 size 1 : (1WP<39>,1L9E)
base 47 step 855573 size 1 : (<40><37><42>A,<41>3<38><42>)
base 48 step 73069 size 1 : (32<36>M,31M<43>)
base 49 step 74365 size 1 : (2<43>L<44>,2<44><43>N)
base 50 step 33473 size 1 : (14<43><43>,135I)
base 51 step 33406 size 1 : (<50><42><38>,10C<45>)

base 52 goes for more than 2,000,000 steps.

I really liked Hans's idea of just tracking the counts and exploring the
space of possibilities.  That's why I've spent so much time playing
around with it.  But I must confess I'm not really that excited by the
sequences themselves.  If someone wants to take the time to enter
them, please do so.

-Dave


> From seqfan-bounces at list.seqfan.eu Wed Aug 20 20:39:10 2014
> From: Hans Havermann <gladhobo at teksavvy.com>
> Date: Wed, 20 Aug 2014 20:38:52 -0400
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Look and say -- my parity

> Yes, the denouement was abrupt. Thank you, David! I have a single count of (102853,99095) at #17187. To put it back into Eric's domain, we have a 17187-term sequence: 22 .. 1028531990952 or 22 .. 9909521028531 with lots of in-between variations. Perhaps if we settle on the smallest possible term (that realizes the full 17187-term sequence) at each location where more than one value is possible, we have a well defined sequence. I don't think I'm up to calculating it.

> On Aug 20, 2014, at 7:26 PM, David Applegate <david at research.att.com> wrote:

> > for my version it terminated with no values at step 17188

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