[seqfan] A269526, an infinite Sudoku-type array

[Neil Sloane]

Dear Seq Fans,  The following is a pretty interesting recent sequence:

Array read by anti-diagonals upwards in which each term is the least
positive value satisfying the condition that no row, column, or diagonal
contains a repeated term.

The sequence is A269526.  I just added the first three rows and the main
diagonal as A274315 ff. (They all need b-files.)

The array begins:

1, 3, 2, 6, 4, 5, 10, 11, 13, 8, 14, 18, 7, 20, 19, ...
2, 4, 5, 1, 8, 3, 6, 12, 14, 16, 7, 15, 17, 9, 22, ...
3, 1, 6, 2, 9, 7, 5, 4, 15, 17, 12, 19, 18, 21, 8, ...
4, 2, 3, 5, 1, 8, 9, 7, 16, 6, 18, 17, 11, 10, 23, ...
5, 7, 1, 4, 2, 6, 3, 15, 9, 10, 13, 8, 20, 14, 12, ...
...

It seems very likely that every row, columns and diagonal (meaning
diagonals parallel to the main diagonal) is a perm of the natural numbers,
but I didn't try to find a proof.

The first col is just 1,2,3,4,... but the next few columns could also be
added as new? entries.

There are a lot of other related sequences, for example, in row n, where
does 1 appear?

It is unusual to see such a nice array which is unrelated to any other
sequence in the OEIS!  (But I didn't try Superseeker).

This looks like a lovely problem crying out to be analyzed.

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