A274821 Hexagonal spiral constructed on the nodes of the infinite triangular net in which each term is the least positive integer such that no diagonal contains a repeated term.

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

Offset: 0

Author

Omar E. Pol, Jul 09 2016

Keywords

• nonn

Comments

Also spiral constructed on the infinite hexagonal grid in which each term is the least positive integer such that no diagonal of successive adjacent cells contains a repeated term. Every number is located in the center of a hexagonal cell. Every cell is also the center of three diagonals of successive adjacent cells.

Examples

			Illustration of initial terms as a spiral:
.
.                  10 - 5 - 3 - 9 - 8
.                  /                 \
.                 9   4 - 7 - 8 - 6   10
.                /   /             \   \
.               3   1   6 - 4 - 5   7   2
.              /   /   /         \   \   \
.            11   7   4   2 - 3   1   5   9
.            /   /   /   /     \   \   \   \
.          12   6   5   3   1 - 2   4   8   7
.            \   \   \   \         /   /   /
.             9   8   6   2 - 3 - 1   7   4
.              \   \   \             /   /
.              10   1   4 - 5 - 7 - 6   2
.                \   \                 /
.                11   7 - 8 - 6 - 5 - 9
.                  \
.                  13 - 4 - 9 - 10 - 8
.
		

Crossrefs

Cf. A269526 (square array), A274640 (square spiral), A274651 (right triangle), A274820, A274920, A274921, A275606, A275610.

Formula

a(n) = A274820(n) + 1.