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A362363
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Arm number of the base spiral in A362249 which visits large spiral point n there.
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3
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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
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OFFSET
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1,3
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COMMENTS
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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).
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LINKS
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FORMULA
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If n is a square:
a(n) = 3*(n+1 mod 2); (a(n) = 3 for even squares).
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EXAMPLE
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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.
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PROG
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(MATLAB)
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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