A282510 Irregular triangle T(n,k) read by rows: Each term is the least positive integer such that no row, column, diagonal, or antidiagonal contains a repeated term; and each row terminates at k when it contains all numbers <= k.

1, 2, 3, 1, 4, 5, 2, 3, 1, 3, 1, 4, 5, 2, 5, 2, 3, 1, 4, 6, 4, 5, 2, 3, 7, 8, 9, 1, 7, 8, 6, 4, 5, 9, 10, 11, 2, 3, 1, 9, 10, 7, 8, 6, 11, 12, 13, 4, 5, 2, 3, 1, 8, 6, 9, 10, 7, 13, 14, 15, 11, 12, 4, 5, 2, 3, 1, 10, 11, 12, 6, 9, 1, 7, 8, 13, 14, 15, 16, 4, 5, 2, 3

Offset: 1

Author

Bob Selcoe, Feb 19 2017

Keywords

• nonn
• tabf

Comments

Similar in construction to A274651; the difference between them is that here, each row terminates at k when it contains all numbers <= k (hence this triangle is irregular, while A274651 is not).

Conjecture: All columns and diagonals are permutations of the natural numbers; a proof will be more involved than for A274651.

Row lengths are not (weakly) monotonically increasing: row 25 has 42 terms, row 26 has 41 terms. Row indices where row lengths decrease are: 26, 64, 144, 199, 326, 400, ... . - Alois P. Heinz, Mar 17 2017

Examples

			Triangle begins:
:  1
:  2  3  1
:  4  5  2  3  1
:  3  1  4  5  2
:  5  2  3  1  4
:  6  4  5  2  3  7  8  9  1
:  7  8  6  4  5  9 10 11  2  3  1
:  9 10  7  8  6 11 12 13  4  5  2  3  1
:  8  6  9 10  7 13 14 15 11 12  4  5  2  3  1
: 10 11 12  6  9  1  7  8 13 14 15 16  4  5  2  3
: 12  7 13 14  8  2  3  1  6 10  9 17 11 15  4  5  16
		

Links

• Alois P. Heinz, Rows n = 1..160, flattened

Crossrefs

Cf. A274651.