A274920 Spiral constructed on the nodes of the triangular net in which each new term is the least nonnegative integers distinct from its neighbors.

0, 1, 2, 1, 2, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 1, 0, 1, 2, 0, 1, 2, 0, 2, 1, 0

Offset: 0

Author

Omar E. Pol, Jul 11 2016

Keywords

• nonn

Comments

The structure of the spiral has the following properties:

1) Positive terms are on the nodes of a hexagonal net.

2) Every 0 is surrounded by three equidistant 1's and three equidistant 2's.

3) Every 1 is surrounded by three equidistant 0's and three equidistant 2's.

4) Every 2 is surrounded by three equidistant 0's and three equidistant 1's.

5) Diagonals are periodic sequences with period 3 (A010872 and A080425).

For the connection with the structure of graphene see also A275606.

Examples

			Illustration of initial terms as a spiral:
.
.                2 - 0 - 1 - 2 - 0 - 1
.               /                     \
.              0   1 - 2 - 0 - 1 - 2   0
.             /   /                 \   \
.            1   2   0 - 1 - 2 - 0   1   2
.           /   /   /             \   \   \
.          2   0   1   2 - 0 - 1   2   0   1
.         /   /   /   /         \   \   \   \
.        0   1   2   0   1 - 2   0   1   2   0
.       /   /   /   /   /     \   \   \   \   \
.      1   2   0   1   2   0 - 1   2   0   1   2
.       \   \   \   \   \         /   /   /   /
.        0   1   2   0   1 - 2 - 0   1   2   0
.         \   \   \   \             /   /   /
.          2   0   1   2 - 0 - 1 - 2   0   1
.           \   \   \                 /   /
.            1   2   0 - 1 - 2 - 0 - 1   2
.             \   \                     /
.              0   1 - 2 - 0 - 1 - 2 - 0
.               \
.                2 - 0 - 1 - 2 - 0 - 1
.
		

Crossrefs

Cf. A010872, A080425, A274820, A274821, A274921, A275606, A275610.

Formula

a(n) = A274921(n) - 1.