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A274921 Spiral constructed on the nodes of the triangular net in which each new term is the least positive integer distinct from its neighbors.

%I A274921 #49 Sep 16 2017 03:45:51
%S A274921 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 A274921 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 A274921 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 A274921 Spiral constructed on the nodes of the triangular net in which each new term is the least positive integer distinct from its neighbors.
%C A274921 The structure of the spiral has the following properties:
%C A274921 1) Every 1 is surrounded by three equidistant 2's and three equidistant 3's.
%C A274921 2) Every 2 is surrounded by three equidistant 1's and three equidistant 3's.
%C A274921 3) Every 3 is surrounded by three equidistant 1's and three equidistant 2's.
%C A274921 4) Diagonals are periodic sequences with period 3 (A010882 and A130784).
%C A274921 From _Juan Pablo Herrera P._, Nov 16 2016: (Start)
%C A274921 5) Every hexagon with a 1 in its center is the same hexagon as the one in the middle of the spiral.
%C A274921 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 A274921 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 A274921 Robert Israel, <a href="/A274921/b274921.txt">Table of n, a(n) for n = 0..10000</a>
%F A274921 a(n) = A274920(n) + 1.
%e A274921 Illustration of initial terms as a spiral:
%e A274921 .
%e A274921 .                3 - 1 - 2 - 3 - 1 - 2
%e A274921 .               /                     \
%e A274921 .              1   2 - 3 - 1 - 2 - 3   1
%e A274921 .             /   /                 \   \
%e A274921 .            2   3   1 - 2 - 3 - 1   2   3
%e A274921 .           /   /   /             \   \   \
%e A274921 .          3   1   2   3 - 1 - 2   3   1   2
%e A274921 .         /   /   /   /         \   \   \   \
%e A274921 .        1   2   3   1   2 - 3   1   2   3   1
%e A274921 .       /   /   /   /   /     \   \   \   \   \
%e A274921 .      2   3   1   2   3   1 - 2   3   1   2   3
%e A274921 .       \   \   \   \   \         /   /   /   /
%e A274921 .        1   2   3   1   2 - 3 - 1   2   3   1
%e A274921 .         \   \   \   \             /   /   /
%e A274921 .          3   1   2   3 - 1 - 2 - 3   1   2
%e A274921 .           \   \   \                 /   /
%e A274921 .            2   3   1 - 2 - 3 - 1 - 2   3
%e A274921 .             \   \                     /
%e A274921 .              1   2 - 3 - 1 - 2 - 3 - 1
%e A274921 .               \
%e A274921 .                3 - 1 - 2 - 3 - 1 - 2
%e A274921 .
%p A274921 A[0]:= 1: A[1]:= 2: A[2]:= 3:
%p A274921 b:= 3: c:= 2: d:= 2: e:= 1: f:= 1:
%p A274921 for n from 3 to 200 do
%p A274921   if n = b then
%p A274921      r:= b; b:= c + d - f + 1; f:= e; e:= d; d:= c; c:= r;
%p A274921      A[n]:= A[n-2];
%p A274921   else
%p A274921      A[n]:= 6 - A[n-1] - A[n-2];
%p A274921   fi
%p A274921 od:
%p A274921 seq(A[i],i=0..200); # _Robert Israel_, Sep 15 2017
%Y A274921 Cf. A001399, A010882, A130784, A253186, A274820, A274821, A274920, A275606, A275610.
%K A274921 nonn
%O A274921 0,2
%A A274921 _Omar E. Pol_, Jul 11 2016