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

0,2

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

Links

Table of n, a(n) for n=0..104.

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.

Formula

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

Example

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).

Crossrefs

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

Sequence in context: A275103 A359729 A107795 * A302795 A272726 A262304

Adjacent sequences: A274914 A274915 A274916 * A274918 A274919 A274920

Keyword

nonn

Author

Omar E. Pol, Jul 11 2016

Status

approved