To generalize or not to generalize...

[Joerg Arndt]

On these two sequences, again some news:

-After his work on Taxicab(6), Uwe Hollerbach (USA) confirmed this week that
my upper bound
	  933528127886302221000
	=  8387730^3 +  7002840^3   (1)
	=  8444345^3 +  6920095^3   (2)
	=  9773330^3 -    84560^3   (3)
	=  9781317^3 -  1318317^3   (4)
	=  9877140^3 -  3109470^3   (5)
	= 10060050^3 -  4389840^3   (6)
	= 10852660^3 -  7011550^3   (7)
	= 18421650^3 - 17454840^3   (8)
	= 41337660^3 - 41154750^3   (9)
	= 77480130^3 - 77428260^3   (10)
constructed in Dec 2006 is really Cabtaxi(10). See his announcement at
http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0805&L=nmbrthry&T=0&P=1284

-better Taxicab(>=11) and Cabtaxi(>=11) upper bounds recently found by
Duncan Moore, Jaroslaw Wroblewski and me.

More details at http://cboyer.club.fr/Taxicab.htm, with updated tables of
Taxicab and Cabtaxi numbers.

Christian.


-----Message d'origine-----
De : Christian Boyer [mailto:cboyer at club-internet.fr] 
Envoyé : lundi 24 mars 2008 12:07
À : seqfan at ext.jussieu.fr
Objet : Taxicab and Cabtaxi numbers (A011541 and A047696)

Two news on these series:
-paper "New Upper Bounds for Taxicab and Cabtaxi numbers" now published in
the Journal of Integer Sequences.
-and Taxicab(6) recently proved by Uwe Hollerbach.

Look at http://cboyer.club.fr/Taxicab.htm

Christian.

 





Hi,
firstly, you may want to teach your mail program
not to trash fromatting/quoting.


* koh <zbi74583 at boat.zero.ad.jp> [May 17. 2008 09:01]:
>     Dear Neil, zak, Joerg, Peter
> 
> 
>     >1000, 47
>     It is one example of parameters b(0), k.
>     1000 is so large that the oscillating part is represented.
> 
>     > There iis a rule that sequences in the OEIS should not depen
>     > on a large but arbitrary parameter.
> 
>     It means many interesting sequences which depend on arbitrary
>     parameter don't exist on OEIS.  It is not good.

Allowing seqs depending on arbitrary parameter would be
a very bad thing!  This is totally agreed upon.

... and I marvel at the fact that A137607 was included
in the database.



> 
>     Then I will add the Generalized GO sequence to OEUAI.
>           http://boat.zero.ad.jp/~zbi74583/OEUAI-04.htm
> 
>     It is my pleasure to update OEUAI.  Because you added almost all
>     sequences which I submitted to OEIS so I could not update OEUAI.
>  
>     >GO 
> 
>     Once I submitted A096259.
>     If both players don't try to win and if they put a stone on the
>     same place when the arrangement of stones are the same then the
>     play becomes periodic.  Because number of the arrangements of
>     stones are finite.  It is 3^361.
> 
>     The sequence gives the longest period for each n points GO board.
>     The origin of Generalized GO sequence is in the formula.
> 
>     >And even the length of the periods is in the EIS as
>           http://www.research.att.com/~njas/sequences/A003558.

Indeed, just checked.


> 
>     It is interesting.
>     Did you send the comment to OEIS?
> 
>     >and 2.) _slightly_ too artificial for my taste ;-)
> 
>     I agree with you.
> 
>     Try to find any property of G.GO sequence and submit the
>     sequence related with it.

Pretty. Please. Don't.


> 
> 
> 
> 
>     Yasutoshi
>     


cheers,   jj