A274917 Square spiral in which each new term is the least positive integer distinct from its (already assigned) eight neighbors.

1, 2, 3, 4, 2, 3, 2, 4, 3, 1, 4, 1, 2, 5, 1, 3, 1, 4, 1, 4, 1, 3, 1, 2, 4, 2, 3, 2, 3, 4, 1, 3, 4, 2, 4, 2, 3, 5, 2, 3, 2, 3, 2, 4, 2, 4, 3, 1, 3, 1, 4, 1, 4, 1, 2, 3, 2, 4, 2, 1, 3, 1, 5, 1, 2, 4, 1, 4, 1, 4, 1, 4, 1, 3, 1, 3, 1, 2, 4, 2, 4, 2, 3, 2, 3, 2, 3, 4, 1, 4, 1, 3, 1, 3, 4, 2, 4, 2, 3, 4, 1, 3, 5, 2, 3

Offset: 0

Author

Omar E. Pol, Jul 11 2016

Keywords

• nonn

Comments

The largest element is 5 and it is also the element with lower density in the spiral.

See A275609 for proof that 5 is maximal and for further comments. - N. J. A. Sloane, Mar 24 2019

Examples

			Illustration of initial terms as a spiral (n = 0..168):
.
.     2 - 3 - 2 - 1 - 5 - 1 - 3 - 1 - 2 - 4 - 2 - 4 - 2
.     |                                               |
.     4   1 - 4 - 3 - 2 - 4 - 2 - 4 - 3 - 1 - 3 - 1   3
.     |   |                                       |   |
.     2   3   2 - 1 - 5 - 1 - 3 - 1 - 2 - 4 - 2   4   2
.     |   |   |                               |   |   |
.     1   5   4   3 - 2 - 4 - 2 - 4 - 3 - 1   3   1   3
.     |   |   |   |                       |   |   |   |
.     4   2   1   5   1 - 3 - 1 - 5 - 2   4   2   4   2
.     |   |   |   |   |               |   |   |   |   |
.     1   3   4   2   4   2 - 4 - 3   1   3   1   3   1
.     |   |   |   |   |   |       |   |   |   |   |   |
.     4   2   1   3   1   3   1 - 2   4   2   4   2   4
.     |   |   |   |   |   |           |   |   |   |   |
.     1   3   4   2   4   2 - 4 - 3 - 1   3   1   3   1
.     |   |   |   |   |                   |   |   |   |
.     4   2   1   3   1 - 3 - 1 - 2 - 4 - 2   4   2   4
.     |   |   |   |                           |   |   |
.     1   3   4   2 - 4 - 2 - 4 - 3 - 1 - 3 - 1   3   1
.     |   |   |                                   |   |
.     4   2   1 - 3 - 1 - 3 - 1 - 2 - 4 - 2 - 4 - 2   4
.     |   |                                           |
.     1   3 - 4 - 2 - 4 - 2 - 4 - 3 - 1 - 3 - 1 - 3 - 1
.     |
.     2 - 5 - 1 - 3 - 1 - 3 - 1 - 2 - 4 - 2 - 4 - 2 - 4
.
a(13) = 5 is the first "5" in the sequence and its four neighbors are 4 (southwest), 3 (south), 1 (southeast) and 2 (east) when a(13) is placed in the spiral.
a(157) = 5 is the 6th "5" in the sequence and it is also the first "5" that is below the NE-SW main diagonal of the spiral (see the second term in the last row of the above diagram).
		

Links

• F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

Crossrefs

Cf. A274913, A274921, A275609, A278354 (number of neighbors).

Formula

a(n) = A275609(n) + 1. - Omar E. Pol, Nov 14 2016