[seqfan] Re: Variation on an infinite Sudoku-type array

Neil Sloane njasloane at gmail.com
Sat Jul 9 19:11:06 CEST 2016


I have added Zak's nice "Spiral" as A274640.

I also added the same sequence with 1 subtracted from every term, see
A274641.

A274640 is the main entry. I added Kerry illustrations.   Needs more terms
and a b-file. Also, the 8 sequences starting at the center and moving
outwards in the 8 compass directions should be added (or cross-referenced
if they already exist).



Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Jul 2, 2016 at 11:49 PM, Zak Seidov <seqfan at list.seqfan.eu> wrote:

>  And you may/wish to submit the SEQ
> 1, 2, 3, 4, 2,3,4,5,6,1,4,6,2,1,6,5,2,3,4,...
> with your great bfile.
> Zak
>
>
> >Воскресенье,  3 июля 2016, 4:53 +03:00 от Kerry Mitchell <
> lkmitch at gmail.com>:
> >
> >Hi Zak,
> >
> >I'm sorry for not acknowledging your idea.  I had already started looking
> >at the spiral when I saw your post, so we're both geniuses!  :-)  I'm glad
> >you like the figures.
> >
> >Kerry
> >
> >On Sat, Jul 2, 2016 at 4:30 PM, Zak Seidov < seqfan at list.seqfan.eu >
> wrote:
> >
> >>
> >> Dear Kerry,
> >> This is exactly my "old spiral",
> >> see my post to [seqfan] 30 june, 14:05 .
> >> Apparently nobody noticed it in the "hectic" thread
> >> "Sudoku-type array":(
> >>
> >> Zak
> >> PS But you've calculated great figures!
> >> While I just mentioned the "idea".
> >> Congrats!
> >>
> >>
> >> >Суббота,  2 июля 2016, 22:36 +03:00 от Kerry Mitchell <
> lkmitch at gmail.com
> >> >:
> >> >
> >> >Hi all,
> >> >
> >> >This is a spinoff from the "A269526, an infinite Sudoku-type array"
> >> thread.
> >> >
> >> >I was intrigued by the idea in the original thread and wanted to try
> some
> >> >variations.  I didn't like the antidiagonals approach because of the
> break
> >> >at the end of a line, jumping down to the next line.  So I tried with a
> >> >square spiral (ala Ulam spiral), so that each newly populated cell is
> >> >adjacent to the previous cell.  Here are the central 121 cells:
> >> >
> >> >09  16  02  04  07  14  11  12  01  05  08
> >> >17  08  15  14  13  12  09  10  06  07  03
> >> >01  02  04  11  10  03  08  07  09  13  15
> >> >08  09  07  03  05  06  01  02  04  12  11
> >> >11  12  08  01  02  04  03  06  05  10  14
> >> >15  07  06  05  03  01  02  04  08  11  12
> >> >14  10  03  02  04  05  06  01  07  09  13
> >> >07  11  09  06  01  02  04  05  03  08  10
> >> >04  13  05  07  08  09  10  11  12  06  01
> >> >12  14  10  09  06  13  05  03  15  16  07
> >> >10  15  01  12  16  08  14  13  11  18  17
> >> >
> >> >The sequence begins with "01" in the center.  Here's a list of those
> >> >values, in order:
> >> >
> >> >1
> >> >2
> >> >3
> >> >4
> >> >2
> >> >3
> >> >4
> >> >5
> >> >6
> >> >1
> >> >4
> >> >6
> >> >2
> >> >1
> >> >6
> >> >5
> >> >3
> >> >1
> >> >5
> >> >2
> >> >6
> >> >1
> >> >2
> >> >4
> >> >5
> >> >3
> >> >7
> >> >8
> >> >5
> >> >4
> >> >9
> >> >7
> >> >8
> >> >3
> >> >10
> >> >11
> >> >4
> >> >7
> >> >8
> >> >6
> >> >3
> >> >9
> >> >5
> >> >7
> >> >8
> >> >9
> >> >10
> >> >11
> >> >12
> >> >6
> >> >8
> >> >9
> >> >11
> >> >10
> >> >12
> >> >13
> >> >7
> >> >6
> >> >10
> >> >9
> >> >12
> >> >13
> >> >14
> >> >15
> >> >8
> >> >2
> >> >9
> >> >12
> >> >7
> >> >10
> >> >11
> >> >13
> >> >14
> >> >10
> >> >9
> >> >6
> >> >13
> >> >5
> >> >3
> >> >15
> >> >16
> >> >7
> >> >1
> >> >10
> >> >13
> >> >12
> >> >14
> >> >11
> >> >15
> >> >3
> >> >8
> >> >5
> >> >1
> >> >12
> >> >11
> >> >14
> >> >7
> >> >4
> >> >2
> >> >16
> >> >9
> >> >17
> >> >1
> >> >8
> >> >11
> >> >15
> >> >14
> >> >7
> >> >4
> >> >12
> >> >10
> >> >15
> >> >1
> >> >12
> >> >16
> >> >8
> >> >14
> >> >13
> >> >11
> >> >18
> >> >17
> >> >
> >> >And here are a couple of images of the sequence.  In the first, the
> colors
> >> >represent the values, from black (small) to white (large).  In the
> second,
> >> >values <= 100 are black and those > 100 are white.
> >> >
> >> > http://www.kerrymitchellart.com/temp/spiral-low.jpg
> >> > http://www.kerrymitchellart.com/temp/spiral-high.jpg
> >> >
> >> >Kerry
> >> >
> >> >--
> >> >Seqfan Mailing list -  http://list.seqfan.eu/
> >>
> >>
> >> --
> >> Seqfan Mailing list -  http://list.seqfan.eu/
> >>
> >
> >--
> >Seqfan Mailing list -  http://list.seqfan.eu/
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>


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