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A163336 Hilbert II curve in N x N grid, starting downwards 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), ... 25
0, 5, 1, 6, 4, 2, 47, 7, 3, 15, 48, 46, 8, 14, 16, 53, 49, 45, 9, 13, 17, 54, 52, 50, 44, 10, 12, 18, 59, 55, 51, 39, 43, 11, 23, 19, 60, 58, 56, 38, 40, 42, 24, 22, 20, 425, 61, 57, 69, 37, 41, 29, 25, 21, 141, 426, 424, 62, 68, 70, 36, 30, 28, 26, 140, 142, 431, 427 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

A. Karttunen, Table of n, a(n) for n = 0..3320

Eric Weisstein's World of Mathematics, Hilbert curve

Wikipedia, Self-avoiding walk

Wikipedia, Space-filling curve (Wikipedia gives this curve as an example of a Peano curve, although this is not the one Peano himself gave).

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

The top left 9x9 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):

+0 +5 +6 47 48 53 54 59 60

+1 +4 +7 46 49 52 55 58 61

+2 +3 +8 45 50 51 56 57 62

15 14 +9 44 39 38 69 68 63

16 13 10 43 40 37 70 67 64

17 12 11 42 41 36 71 66 65

18 23 24 29 30 35 72 77 78

19 22 25 28 31 34 73 76 79

20 21 26 27 32 33 74 75 80

CROSSREFS

Transpose: A163334. Inverse: A163337. a(n) = A163332(A163330(n)) = A163327(A163333(A163328(n))) = A163334(A061579(n)). One-based version: A163340. Row sums: A163342. Row 0: A163481. Column 0: A163480. Central diagonal: A163343. See A163357 & A163359 for other Hilbert curves.

Sequence in context: A077491 A086231 A201419 * A173898 A200644 A318265

Adjacent sequences:  A163333 A163334 A163335 * A163337 A163338 A163339

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Jul 29 2009

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)