A368122 a(n) is the x-coordinate of the n-th point in a square spiral mapped to a square grid rotated by Pi/4 using the symmetrized variant of the distance-limited strip bijection described in A368121.

0, 1, 0, -1, -1, -1, 0, 1, 1, 2, 2, 1, 0, 0, -1, -2, -3, -2, -2, -1, 0, 0, 1, 2, 3, 3, 3, 2, 2, 1, 0, -1, -2, -2, -3, -3, -4, -3, -3, -2, -2, -1, 0, 1, 2, 2, 3, 3, 4, 5, 4, 4, 3, 2, 1, 1, 0, 0, -1, -2, -3, -4, -4, -5, -6, -5, -4, -4, -3, -2, -1, -1, 0, 0, 1, 2, 3, 4, 4, 5, 6, 6, 5, 5, 5, 4

Offset

0,10

Links

Hugo Pfoertner, Table of n, a(n) for n = 0..3000

Hugo Pfoertner, Plot of mapped spiral, using Plot 2.

Index entries for sequences related to coordinates of 2D curves

Prog

(PARI) \\ ax(n), ay(n) after Kevin Ryde's functions in A174344 and A274923.
\\ It is assumed that the PARI programs from A367150 and A368121 have been loaded and the functions defined there are available.
ax(n) = {my (m=sqrtint(n), k=ceil(m/2)); n -= 4*k^2; if (n<0, if (n<-m, k, -k-n), if (n<m, -k, n-3*k))};
ay(n) = {my (m=sqrtint(n), k=ceil(m/2)); n -= 4*k^2; if (n<0, if (n<-m, 3*k+n, k), if (n<m, k-n, -k))};
a368122(n) = BijectionD([ax(n), ay(n)], BijectionK)[1];

Crossrefs

A368123 gives the corresponding y-coordinates.

Cf. A367150, A368121, A368127, A368128.

Analogous pair of sequences, but without symmetrization: A367895, A367896.

Sequence in context: A051168 A367895 A368127 * A281459 A163528 A329054

Adjacent sequences: A368119 A368120 A368121 * A368123 A368124 A368125

Keyword

sign

Author

Hugo Pfoertner, Jan 06 2024

Status

approved