A343631 X-coordinate of the points following the 3D spiral defined in A343630.

0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 1, -1, -1, 1, 1, 0, -1, 0, 1, -1, -1, 1, 1, -1, -1, 1, 0, 2, 0, -2, 0, 0, 1, 0, -1, 0, 2, 0, -2, 0, 2, 1, -1, -2, -2, -1, 1, 2, 2, 0, -2, 0, 0, 0, 1, -1, 1, -1, -1, 1, 2, 1, -1, -2, -2, -1, 1, 2, 2, 1, -1, -2, -2, -1, 1, 2, 1, -1, -1, 1, 2, 0, -2, 0, 2, -2, -2, 2, 2, 0, -2, 0, 0, 2, 1, -1, -2, -2, -1, 1, 2, 2, -2, -2, 2, 3, 0, -3, 0

Offset: 0

Author

M. F. Hasler, Apr 28 2021

Keywords

• sign

Comments

See the main entry A343630 for details about this 3D generalization of an Ulam type spiral using the Euclidean norm.

Sequences A343632 and A343633 give the y and z coordinates.

The sequence can be seen as a table with row lengths 3*A005875, where A005875(r) is the number of points at distance sqrt(r) from the origin.

Sequence A343641 is the analog for the square spiral variant A343640.

Crossrefs

Cf. A343632, A343633 (list of y and z-coordinates).

Cf. A343641 (variant using the sup norm => square spiral).

Cf. A342561 (variant which scans each sphere by increasing z).

Cf. A005875 (number of points on a shell with given radius).

Cf. A004215 (numbers that can't be written as sum of 3 squares => empty shells).

Programs

PARI

d=1; A343631_vec=concat([[P[1] | P<-S=A343630_row(n,d)]+(#S&&!d*=-1) | n<-[0..8]]) \\ the variable d is necessary to correct the z-scan direction in rows between A004215(2k-1) and A004215(2k).