A274921 - OEIS

%I #49 Sep 16 2017 03:45:51

%S 1,2,3,2,3,2,3,1,3,1,2,1,3,1,2,1,3,1,2,3,2,1,2,3,1,3,2,1,2,3,1,3,2,1,

%T 2,3,1,2,1,3,2,3,1,2,3,2,1,3,2,3,1,2,3,2,1,3,2,3,1,2,3,1,3,2,1,3,1,2,

%U 3,1,2,1,3,2,1,3,1,2,3,1,2,1,3,2,1,3,1,2,3,1,2,3,2,1,3,2,1,2,3,1,2,3,1,3,2,1

%N Spiral constructed on the nodes of the triangular net in which each new term is the least positive integer distinct from its neighbors.

%C The structure of the spiral has the following properties:

%C 1) Every 1 is surrounded by three equidistant 2's and three equidistant 3's.

%C 2) Every 2 is surrounded by three equidistant 1's and three equidistant 3's.

%C 3) Every 3 is surrounded by three equidistant 1's and three equidistant 2's.

%C 4) Diagonals are periodic sequences with period 3 (A010882 and A130784).

%C From _Juan Pablo Herrera P._, Nov 16 2016: (Start)

%C 5) Every hexagon with a 1 in its center is the same hexagon as the one in the middle of the spiral.

%C 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)

%C 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

%H Robert Israel, <a href="/A274921/b274921.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A274920(n) + 1.

%e Illustration of initial terms as a spiral:

%e .

%e .                3 - 1 - 2 - 3 - 1 - 2

%e .               /                     \

%e .              1   2 - 3 - 1 - 2 - 3   1

%e .             /   /                 \   \

%e .            2   3   1 - 2 - 3 - 1   2   3

%e .           /   /   /             \   \   \

%e .          3   1   2   3 - 1 - 2   3   1   2

%e .         /   /   /   /         \   \   \   \

%e .        1   2   3   1   2 - 3   1   2   3   1

%e .       /   /   /   /   /     \   \   \   \   \

%e .      2   3   1   2   3   1 - 2   3   1   2   3

%e .       \   \   \   \   \         /   /   /   /

%e .        1   2   3   1   2 - 3 - 1   2   3   1

%e .         \   \   \   \             /   /   /

%e .          3   1   2   3 - 1 - 2 - 3   1   2

%e .           \   \   \                 /   /

%e .            2   3   1 - 2 - 3 - 1 - 2   3

%e .             \   \                     /

%e .              1   2 - 3 - 1 - 2 - 3 - 1

%e .               \

%e .                3 - 1 - 2 - 3 - 1 - 2

%e .

%p A[0]:= 1: A[1]:= 2: A[2]:= 3:

%p b:= 3: c:= 2: d:= 2: e:= 1: f:= 1:

%p for n from 3 to 200 do

%p   if n = b then

%p      r:= b; b:= c + d - f + 1; f:= e; e:= d; d:= c; c:= r;

%p      A[n]:= A[n-2];

%p   else

%p      A[n]:= 6 - A[n-1] - A[n-2];

%p   fi

%p od:

%p seq(A[i],i=0..200); # _Robert Israel_, Sep 15 2017

%Y Cf. A001399, A010882, A130784, A253186, A274820, A274821, A274920, A275606, A275610.

%K nonn

%O 0,2

%A _Omar E. Pol_, Jul 11 2016