A368127 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 A368126.

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

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 A368126 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))};
a368127(n) = BijectionD([ax(n), ay(n)], Bijectionk)[1];

Crossrefs

A368128 gives the corresponding y-coordinates.

Cf. A367150, A368126.

Analogous sequences, but without symmetrization: A367895, A367896.

Sequence in context: A219489 A051168 A367895 * A368122 A281459 A163528

Adjacent sequences: A368124 A368125 A368126 * A368128 A368129 A368130

Keyword

sign

Author

Hugo Pfoertner, Jan 07 2024

Status

approved