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

0,2

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.

Links

Table of n, a(n) for n=0..99.

Formula

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

Example

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.

Sequence in context: A339601 A117666 A274921 * A275720 A307200 A339092

Adjacent sequences: A274818 A274819 A274820 * A274822 A274823 A274824

Keyword

nonn

Author

Omar E. Pol, Jul 09 2016

Status

approved