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A274917
Square spiral in which each new term is the least positive integer distinct from its (already assigned) eight neighbors.
3
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jul 11 2016
STATUS
approved