A339455 a(n) is the X-coordinate of the n-th point of the space filling curve H defined in Comments section; A339456 gives Y-coordinates.

0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 4, 3, 2, 3, 2, 3, 3, 3, 4, 3, 4, 3, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 4, 3, 2, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4

Offset

0,7

Comments

We consider a hexagonal lattice with X-axis and Y-axis as follows:

Y

/

/

0 ---- X

We define the family {H_n, n > 0} as follows:

- T_1 contains the origin (0, 0) and (1, 0), in that order:

+-->--+

O

- for any n > 0, H_{n+1} is built from 4 copies of H_n connected with 2^(n+1) unit segments as follows:

+->-2->-+

\ /

^ v

\ /

+->-1->-+->-4->-+

O / \

v ^

/ \

+->-3->-+

- H is the limit of H_n as n tends to infinity,

- H visits once every unit segment (u, v) where u and v are lattice points and at least one of u or v belongs to the region { (x, y) | x > 0 or x + y > 0 },

- the n-th segment of curve H has length 2^A235127(n).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..3008

Rémy Sigrist, Illustration of H_3

Rémy Sigrist, PARI program for A339455

Index entries for sequences related to coordinates of 2D curves

Prog

(PARI) See Links section.

Crossrefs

Cf. A235127, A339456.

Sequence in context: A165472 A228109 A318682 * A123724 A107016 A318702

Adjacent sequences: A339452 A339453 A339454 * A339456 A339457 A339458

Keyword

nonn

Author

Rémy Sigrist, Dec 06 2020

Status

approved