A367895 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 variant of the distance-limited strip bijection described in A367150.

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

Offset

0,10

Links

Rainer Rosenthal, Table of n, a(n) for n = 0..3000

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

Hugo Pfoertner, Visualization of spiral, (orange) and bijection partners from the 2 grids.

Hugo Pfoertner, Comparison of the spirals. This sequence: black, A362955: red.

Prog

(PARI) \\ ax(n), ay(n) after Kevin Ryde's functions in A174344 and A274923.
\\ It is assumed that the PARI program from A367150 has 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))};
a367895(n) = BijectionD([ax(n), ay(n)])[1]

Crossrefs

A367896 gives the corresponding y-coordinates.

Cf. A307110, A362955, A362956, A367150.

Sequence in context: A323258 A219489 A051168 * A368127 A368122 A281459

Adjacent sequences: A367892 A367893 A367894 * A367896 A367897 A367898

Keyword

sign

Author

Hugo Pfoertner and Rainer Rosenthal, Dec 04 2023

Status

approved