A343633 Z-coordinate of the points following the 3D spiral defined in A343630.

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

Offset

0,28

Comments

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

Sequences A343631 and A343632 give the x and y-coordinates.

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

Sequence A343643 is the analog for the square spiral variant A343640.

Links

Table of n, a(n) for n=0..106.

Prog

(PARI) d=1; A343633_vec=concat([[P[3] | P<-S=A343630_row(n, d)]+(#S&&!d*=-1) | n<-[0..9]]) \\ the variable d is necessary to correct the z-scan direction in rows between A004215(2k-1) and A004215(2k).

Crossrefs

Cf. A343631, A343633 (list of x and z-coordinates).

Cf. A343643 (variant using the sup norm => square spiral).

Cf. A342563 (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).

Sequence in context: A110177 A036273 A342563 * A174469 A357724 A297934

Adjacent sequences: A343630 A343631 A343632 * A343634 A343635 A343636

Keyword

sign

Author

M. F. Hasler, Apr 28 2021

Status

approved