A339456 -id:A339456 - cp's OEIS frontend

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

Rémy Sigrist, Dec 06 2020

nonn

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).

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

Cf. A235127, A339456.

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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.

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