A282510 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

LINKS

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

EXAMPLE

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