A334049 Triangular array read by rows in which each term is the least positive integer satisfying the condition that no row, diagonal, or antidiagonal contains a repeated term.

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

Offset: 1

Author

Alec Jones and Peter Kagey, Sep 06 2020

Keywords

• nonn
• tabf

Comments

An infinite Sudoku-type array.

Here, "diagonal" means a diagonal line with an inclination of -60 degrees, and "antidiagonal" means a diagonal line with an inclination of 60 degrees. Thus, the index-7 cell is in the same row as prior cells of indices 5 and 6, in the same diagonal as prior cells of indices 2 and 6, and in the same antidiagonal as the prior cell of index 4.

Triangular tiling is indexed as follows:

*

/ \

/ 1 \

*-----*

/ \ 3 / \

/ 2 \ / 4 \

*-----*-----*

/ \ 6 / \ 8 / \

/ 5 \ / 7 \ / 9 \

*-----*-----*-----*

Examples

			Triangle begins:
           *
          / \
         / 1 \
        *-----*
       / \ 3 / \
      / 2 \ / 4 \
     *-----*-----*
    / \ 5 / \ 2 / \
   / 4 \ / 1 \ / 6 \
  *-----*-----*-----*
		

Links

• Alec Jones, Table of n, a(n) for n = 1..5000

Crossrefs

Triangular tiling analog of A269526.

Cf. A274821.