A362363 Arm number of the base spiral in A362249 which visits large spiral point n there.

0, 0, 2, 3, 0, 0, 0, 1, 0, 1, 2, 0, 2, 2, 0, 3, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 3, 0, 3, 0, 3, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 3, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 2

Offset: 1

Author

Tamas Sandor Nagy and Thomas Scheuerle, Apr 17 2023

Keywords

• nonn

Comments

Arms are numbered 0,1,2,3 for the base spirals with first segment directed East, South, West, North, respectively.

This numbering is successive arms around in the same direction that the spirals themselves turn (both clockwise in the diagrams in A362249).

Examples

			a(5) = 0 because A362249(5) = 13 that is on spiral "E", which is encoded here as 0.
a(8) = 1 because A362249(8) = 58 that is on spiral "S", which is encoded here as 1.
a(11) = 2 because A362249(11) = 139 that is on spiral "W", which is encoded here as 2.
a(34) = 3 because A362249(34) = 1000 that is on spiral "N", which is encoded here as 3.
		

Crossrefs

Cf. A362249, A362265 (indices of 0's).

Programs

MATLAB

function a  = A362363( max_n )
    E = [0 ; 0]; S = [0 ; 0]; W = [0 ; 0]; N = [0 ; 0]; V = [0 0];
    for k = 1:4*max_n
        l = V(1+mod(k+1,2)); s = (-1)^floor(k/2);
        for m = l+(1*s):s:s*k
            V(1+mod(k+1,2)) = m; V2 = V(end:-1:1).*[-1 1];
            N = [N V2']; E = [E V']; S = [S -V2']; W = [W -V'];
        end
    end
    for n = 2:max_n
        [th,r] = cart2pol(E(1,n), E(2,n));
        rot = [cos(-th) -sin(-th); sin(-th) cos(-th)];
        v = E(:,n)'*rot*r;
        jE = find(sum(abs([E(1,:)-v(1); E(2,:)-v(2)]),1) < 0.5);
        jS = find(sum(abs([S(1,:)-v(1); S(2,:)-v(2)]),1) < 0.5);
        jW = find(sum(abs([W(1,:)-v(1); W(2,:)-v(2)]),1) < 0.5);
        jN = find(sum(abs([N(1,:)-v(1); N(2,:)-v(2)]),1) < 0.5);
        a(n-1) = find([length(jE) length(jS) length(jW) length(jN)] > 0) - 1;
    end
end % Thomas Scheuerle, Apr 19 2023

Formula

If n is a square:

a(n) = 3*(n+1 mod 2); (a(n) = 3 for even squares).