[seqfan] Variation on an infinite Sudoku-type array

Kerry Mitchell lkmitch at gmail.com
Sat Jul 2 21:36:58 CEST 2016


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


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