A275606 Spiral constructed on the nodes of the triangular net such that a(n) = signum(A274920(n)).

0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0

Offset

0

Comments

The structure of the spiral has the following properties:

1) The 1's represent the nodes of the hexagonal net.

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

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

4) Diagonals are periodic sequences with period 3 (A011655).

Also the 1's represent the atoms of carbon in graphene.

Links

Table of n, a(n) for n=0..105.

Wikipedia, Graphene

Formula

a(n) = A057427(A274920(n)).

Example

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

Crossrefs

Cf. A011655, A057427, A274820, A274821, A274920, A274921, A275610.

Sequence in context: A097325 A242647 A167393 * A106549 A075897 A135947

Adjacent sequences: A275603 A275604 A275605 * A275607 A275608 A275609

Keyword

nonn

Author

Omar E. Pol, Nov 09 2016

Status

approved