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

1,2

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 \

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

Links

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

Example

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

Crossrefs

Triangular tiling analog of A269526.

Cf. A274821.

Sequence in context: A305594 A320778 A353948 * A058277 A065852 A303998

Adjacent sequences: A334046 A334047 A334048 * A334050 A334051 A334052

Keyword

nonn,tabf

Author

Alec Jones and Peter Kagey, Sep 06 2020

Status

approved