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

1,3

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).

Links

Table of n, a(n) for n=1..87.

Formula

If n is a square:

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A292256 A095750 A056966 * A037846 A037882 A024865

Adjacent sequences: A362360 A362361 A362362 * A362364 A362365 A362366

Keyword

nonn

Author

Tamas Sandor Nagy and Thomas Scheuerle, Apr 17 2023

Status

approved