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A268038 List of y-coordinates of point moving in clockwise square spiral. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,13
COMMENTS
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
LINKS
EXAMPLE
Sequence gives y-coordinate of the n-th point of the following spiral:
.
20--21--22--23--24--25
| |
19 6---7---8---9 26
| | | |
18 5 0---1 10 27
| | | | |
17 4---3---2 11 28
| | |
16--15--14--13--12 29
|
35--34--33--32--31--30
MATHEMATICA
a[n_] := a[n] = If[n==0, 0, a[n-1] + Cos[Mod[Floor[Sqrt[4*(n-1) + 1]], 4]* Pi/2]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 11 2018, after Seppo Mustonen *)
PROG
(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
CROSSREFS
A174344 gives sequence of x-coordinates.
This is the negative of A274923.
The (x,y) coordinates for a point sweeping a quadrant by antidiagonals are (A025581, A002262). - N. J. A. Sloane, Jul 17 2018
Sequence in context: A125088 A226456 A343642 * A274923 A249071 A231713
KEYWORD
sign,easy
AUTHOR
Peter Kagey, Jan 24 2016
STATUS
approved

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Last modified February 21 12:33 EST 2024. Contains 370235 sequences. (Running on oeis4.)