OFFSET
0,2
COMMENTS
The structure of the spiral has the following properties:
1) Every 1 is surrounded by three equidistant 2's and three equidistant 3's.
2) Every 2 is surrounded by three equidistant 1's and three equidistant 3's.
3) Every 3 is surrounded by three equidistant 1's and three equidistant 2's.
From Juan Pablo Herrera P., Nov 16 2016: (Start)
5) Every hexagon with a 1 in its center is the same hexagon as the one in the middle of the spiral.
6) Every triangle whose number of numbers is divisible by 3 has the same number of 1's, 2's, and 3's. For example, a triangle with 6 numbers, has two 1's, two 2's, and two 3's. (End)
a(n) = a(n-2) if n > 2 is in A014591, otherwise a(n) = 6 - a(n-1)-a(n-2). - Robert Israel, Sep 15 2017
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = A274920(n) + 1.
EXAMPLE
Illustration of initial terms as a spiral:
.
. 3 - 1 - 2 - 3 - 1 - 2
. / \
. 1 2 - 3 - 1 - 2 - 3 1
. / / \ \
. 2 3 1 - 2 - 3 - 1 2 3
. / / / \ \ \
. 3 1 2 3 - 1 - 2 3 1 2
. / / / / \ \ \ \
. 1 2 3 1 2 - 3 1 2 3 1
. / / / / / \ \ \ \ \
. 2 3 1 2 3 1 - 2 3 1 2 3
. \ \ \ \ \ / / / /
. 1 2 3 1 2 - 3 - 1 2 3 1
. \ \ \ \ / / /
. 3 1 2 3 - 1 - 2 - 3 1 2
. \ \ \ / /
. 2 3 1 - 2 - 3 - 1 - 2 3
. \ \ /
. 1 2 - 3 - 1 - 2 - 3 - 1
. \
. 3 - 1 - 2 - 3 - 1 - 2
.
MAPLE
A[0]:= 1: A[1]:= 2: A[2]:= 3:
b:= 3: c:= 2: d:= 2: e:= 1: f:= 1:
for n from 3 to 200 do
if n = b then
r:= b; b:= c + d - f + 1; f:= e; e:= d; d:= c; c:= r;
A[n]:= A[n-2];
else
A[n]:= 6 - A[n-1] - A[n-2];
fi
od:
seq(A[i], i=0..200); # Robert Israel, Sep 15 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jul 11 2016
STATUS
approved