[seqfan] Re: Problem reproducing A019989, A019990, and A019991

[Marc LeBrun]

Sean, thanks but actually, Gosper just explicitly told us what he was doing (I'll recopy that part at the end of this reply).
I think some of the confusion is because the OEIS description transcribes Macsyma's *set* union() operators as "ORs".
(see https://people.eecs.berkeley.edu/~fateman/macsyma/docs/refman16.pdf <https://people.eecs.berkeley.edu/~fateman/macsyma/docs/refman16.pdf> page 20)
I'm also unsure about mapping RWG's +/-1's to OEIS's floor -- I'm alas too hurried right now to "poofread" it properly.
Anyway I think there's enough here now to reconstruct the correct algorithm...  "Enjoy"!
[RWG's Macsyma snippet follows]:
========
(c236) abc\a\b\c1(a,b,c,\a,\b,\c):=
  [union(3*a,3*\c+1,3*\b-1),union(3*b,3*\c-1,3*\a+1),union(3*c,3*\b+1,3*\a-1),
   union(3*\a,3*c-1,3*b+1),union(3*\b,3*c+1,3*a-1),union([1],3*\c,3*a+1,3*b-1)];

(d236) abcABC1(a, b, c, A, B, C) := [union(3 a, 3 C + 1, 3 B - 1), 

union(3 b, 3 C - 1, 3 A + 1), union(3 c, 3 B + 1, 3 A - 1), 

union(3 A, 3 c - 1, 3 b + 1), union(3 B, 3 c + 1, 3 a - 1), 

union([1], 3 C, 3 a + 1, 3 b - 1)]

Initialize six empty lists:
(c237) makelist([],k,1,6);
(d237)                     [[], [], [], [], [], []]

Then iteratively apply abcABC1,
...
========

> On Apr 15, 2019, at 11:39 AM, Sean A. Irvine <sairvin at gmail.com> wrote:
> 
> On Tue, 16 Apr 2019 at 03:30, Marc LeBrun <mlb at well.com> wrote:
> 
>> 
>> To break the symmetry perhaps some of those operations don't commute or
>> associate and/or maybe they are computations done sequentially, instead of
>> simultaneous relations?
>> (And, agreed, moreover there STILL needs to be a "1 --> 0" to keep things
>> from saturating.)
>> 
> 
> Some good ideas there.  I certainly had been assuming that the operations
> were simultaneous.  Perhaps there is also some additional special relation
> between a and A, b and B, c and C, otherwise why not simply label the later
> functions d, e, f.
> 
> I did also try a 3-way XOR, i.e. only true if exactly one of the arguments
> true.  But so far everything I have tried results in all functions becoming
> 1 or 0 eventually.
> 
> Sean.
> 
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