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A278354
Number of neighbors of each new term in a square spiral.
6
0, 1, 2, 3, 2, 3, 2, 4, 3, 2, 4, 3, 2, 4, 4, 3, 2, 4, 4, 3, 2, 4, 4, 4, 3, 2, 4, 4, 4, 3, 2, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4
OFFSET
1,3
COMMENTS
Here the "neighbors" of a(n) are defined to be the adjacent elements to a(n) in the same row, column or diagonals, that are present in the spiral when a(n) is the new element of the sequence in progress.
For the same idea but for a right triangle see A278317; for an isosceles triangle see A275015; for a square array see A278290; and for a hexagonal spiral see A047931.
FORMULA
From Robert Israel, Nov 22 2016: (Start)
a(n) = 3 if n>=4 is in A002620.
a(n) = 2 if n>=2 is in A033638.
Otherwise, a(n) = 4 if n > 2. (End)
EXAMPLE
Illustration of initial terms as a spiral (n = 1..169):
.
. 2 - 3 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 2
. | |
. 4 2 - 3 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 2 3
. | | | |
. 4 4 2 - 3 - 4 - 4 - 4 - 4 - 4 - 4 - 2 3 4
. | | | | | |
. 4 4 4 2 - 3 - 4 - 4 - 4 - 4 - 2 3 4 4
. | | | | | | | |
. 4 4 4 4 2 - 3 - 4 - 4 - 2 3 4 4 4
. | | | | | | | | | |
. 4 4 4 4 4 2 - 3 - 2 3 4 4 4 4
. | | | | | | | | | | | |
. 4 4 4 4 4 3 0 - 1 4 4 4 4 4
. | | | | | | | | | | |
. 4 4 4 4 3 2 - 4 - 3 - 2 4 4 4 4
. | | | | | | | | |
. 4 4 4 3 2 - 4 - 4 - 4 - 3 - 2 4 4 4
. | | | | | | |
. 4 4 3 2 - 4 - 4 - 4 - 4 - 4 - 3 - 2 4 4
. | | | | |
. 4 3 2 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 3 - 2 4
. | | |
. 3 2 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 3 - 2
. |
. 2 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 3
.
MAPLE
0, 1, seq(op([2, 4$floor(i/2), 3]), i=0..30); # Robert Israel, Nov 22 2016
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 19 2016
STATUS
approved