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

Author

Hugo Pfoertner and Rainer Rosenthal, Dec 04 2023

Keywords

• sign

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.

Crossrefs

A367896 gives the corresponding y-coordinates.

Cf. A307110, A362955, A362956, A367150.

Programs

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