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A163357 Hilbert curve in N X N grid, starting rightwards from the top-left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... 38
0, 1, 3, 14, 2, 4, 15, 13, 7, 5, 16, 12, 8, 6, 58, 19, 17, 11, 9, 57, 59, 20, 18, 30, 10, 54, 56, 60, 21, 23, 29, 31, 53, 55, 61, 63, 234, 22, 24, 28, 32, 52, 50, 62, 64, 235, 233, 25, 27, 35, 33, 51, 49, 67, 65, 236, 232, 230, 26, 36, 34, 46, 48, 68, 66, 78, 239, 237, 231 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

A. Karttunen, Table of n, a(n) for n = 0..32895

Eric Weisstein's World of Mathematics, Hilbert curve

Wikipedia, Self-avoiding walk

Wikipedia, Space-filling curve

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A163355(A054238(n)).

EXAMPLE

The top left 8 X 8 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):

   0  1 14 15 16 19 20 21

   3  2 13 12 17 18 23 22

   4  7  8 11 30 29 24 25

   5  6  9 10 31 28 27 26

  58 57 54 53 32 35 36 37

  59 56 55 52 33 34 39 38

  60 61 50 51 46 45 40 41

  63 62 49 48 47 44 43 42

CROSSREFS

Transpose: A163359. Inverse: A163358. One-based version: A163361. Row sums: A163365. Row 0: A163482. Column 0: A163483. Central diagonal: A062880. See also A163334 & A163336 for other Hilbert curves.

See also: A163540, A163542, A163547, A163898-A163900, A163538, A163539, A163904, A163907, A163917.

Sequence in context: A157323 A016549 A147584 * A179087 A217013 A058991

Adjacent sequences:  A163354 A163355 A163356 * A163358 A163359 A163360

KEYWORD

nonn,tabl,look

AUTHOR

Antti Karttunen, Jul 29 2009. Links to further derived sequences added Sep 21 2009.

STATUS

approved

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Last modified December 12 21:50 EST 2017. Contains 295954 sequences.