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A268038
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List of y-coordinates of point moving in clockwise square spiral.
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15
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0, 0, -1, -1, -1, 0, 1, 1, 1, 1, 0, -1, -2, -2, -2, -2, -2, -1, 0, 1, 2, 2, 2, 2, 2, 2, 1, 0, -1, -2, -3, -3, -3, -3, -3, -3, -3, -2, -1, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0, -1, -2, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -3, -2, -1, 0, 1, 2, 3, 4, 4, 4
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refs;
listen;
history;
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OFFSET
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1,13
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COMMENTS
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This spiral, in either direction, is sometimes called the "Ulam spiral", but "square spiral" is a better name. (Ulam looked at the positions of the primes, but of course the spiral itself must be much older.) - N. J. A. Sloane, Jul 17 2018
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LINKS
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EXAMPLE
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Sequence gives y-coordinate of the n-th point of the following spiral:
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20--21--22--23--24--25
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19 6---7---8---9 26
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18 5 0---1 10 27
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17 4---3---2 11 28
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16--15--14--13--12 29
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35--34--33--32--31--30
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MATHEMATICA
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a[n_] := a[n] = If[n==0, 0, a[n-1] + Cos[Mod[Floor[Sqrt[4*(n-1) + 1]], 4]* Pi/2]];
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PROG
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(PARI) L=1; d=-1;
for(r=1, 9, d=-d; k=floor(r/2)*d; for(j=1, L++, print1(k, ", ")); forstep(j=k-d, -floor((r+1)/2)*d+d, -d, print1(j, ", "))) \\ Hugo Pfoertner, Jul 28 2018
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CROSSREFS
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A174344 gives sequence of x-coordinates.
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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