A163334 -id:A163334 - cp's OEIS frontend

A163528 The X-coordinate of the n-th point in the Peano curve A163334.

0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 3, 4, 5, 6, 7, 8, 8, 7, 6, 6, 7, 8, 8, 7, 6, 6, 7, 8, 8, 7, 6, 5, 4, 3, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 3, 4, 5, 6, 7, 8, 8, 7, 6, 6, 7, 8, 9, 10, 11, 11, 10, 9, 9, 10, 11, 12, 13, 14, 14, 13, 12

Offset: 0

Antti Karttunen, Aug 01 2009

nonn

There is a 2-state automaton that accepts exactly those pairs (n,a(n)) where n is represented in base 9 and a(n) in base 3; see accompanying file a163528.pdf - Jeffrey Shallit, Aug 10 2023

Antti Karttunen, Table of n, a(n) for n = 0..59048
Jeffrey Shallit, Automaton for A163528
Index entries for sequences related to coordinates of 2D curves

Cf. A025581, A163335, A002262, A163337, A163325, A163332.

See also: A059252, A059253, A163529, A163530, A163531, A163532.

a(n) = A025581(A163335(n)) = A002262(A163337(n)) = A163325(A163332(n)).

Name corrected by Kevin Ryde, Aug 28 2020

A163529 The Y-coordinate of the n-th point in the Peano curve A163334.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8

Offset: 0

Antti Karttunen, Aug 01 2009

There is a 2-state automaton that accepts exactly those pairs (n,a(n)) where n is represented in base 9 and a(n) in base 3; see accompanying file a163529.pdf. - Jeffrey Shallit, Aug 10 2023

Antti Karttunen, Table of n, a(n) for n = 0..59048
Jeffrey Shallit, Automaton for A163529
Index entries for sequences related to coordinates of 2D curves

Cf. A002262, A163335, A025581, A163337, A163326, A163332.

Cf. A059252, A059253, A163528, A163530, A163531, A163533.

a(n) = A002262(A163335(n)) = A025581(A163337(n)) = A163326(A163332(n)).

Name corrected by Kevin Ryde, Aug 28 2020

A163335 Inverse permutation to A163334.

Original entry on oeis.org

0, 1, 3, 7, 4, 2, 5, 8, 12, 17, 23, 30, 22, 16, 11, 6, 10, 15, 21, 28, 36, 46, 37, 29, 38, 47, 57, 69, 58, 48, 59, 70, 82, 96, 83, 71, 60, 50, 41, 32, 40, 49, 39, 31, 24, 18, 13, 9, 14, 19, 25, 33, 26, 20, 27, 34, 42, 52, 43, 35, 44, 53, 63, 74, 86, 99, 85, 73, 62, 51, 61, 72

Offset: 0

Antti Karttunen, Jul 29 2009

nonn

abs(A025581(a(n+1)) - A025581(a(n))) + abs(A002262(a(n+1)) - A002262(a(n))) = 1 for all n.

Inverse: A163334. a(n) = A163329(A163332(n)). One-based version: A163339. See also A163337, A163358.

A163531 The square of the distance from the origin to the n-th point in the Peano curve A163334.

Original entry on oeis.org

0, 1, 4, 5, 2, 1, 4, 5, 8, 13, 20, 29, 26, 17, 10, 9, 16, 25, 36, 49, 64, 65, 50, 37, 40, 53, 68, 73, 58, 45, 52, 65, 80, 89, 74, 61, 50, 41, 34, 25, 32, 41, 34, 25, 18, 13, 10, 9, 16, 17, 20, 29, 26, 25, 36, 37, 40, 53, 50, 49, 64, 65, 68, 73, 80, 89, 74, 65, 58, 45, 52, 61

Offset: 0

Antti Karttunen, Aug 01 2009

nonn

Antti Karttunen, Table of n, a(n) for n = 0..59048

A163534 The absolute direction (0=east, 1=south, 2=west, 3=north) of the Peano curve A163334 at point n.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 01 2009

nonn

Taking every ninth term gives the same sequence: (and similarly for all higher powers of 9 as well): a(n) = a(9*n).

Antti Karttunen, Table of n, a(n) for n = 1..59049

Cf. A163535 (transposed direction), A163536 (turn).

(define (A163534 n) (modulo (+ 3 (A163532 n) (A163533 n) (abs (A163533 n))) 4))

a(n) = A010873(A163532(n)+A163533(n)+abs(A163533(n))+3).

a(n) = A004442(A163535(n)).

Name corrected by Kevin Ryde, Aug 29 2020

A163536 The relative direction (0=straight ahead, 1=turn right, 2=turn left) of the Peano curve A163334 at point n.

Original entry on oeis.org

0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2

Offset: 1

Antti Karttunen, Aug 01 2009

nonn

a(9*n) = a(81*n) for all n.

Antti Karttunen, Table of n, a(n) for n = 1..59049

Cf. A163534 (direction), A163537 (transposed relative).

(define (A163536 n) (A163241 (modulo (- (A163534 (1+ n)) (A163534 n)) 4)))

a(n) = A163241((A163534(n+1)-A163534(n)) modulo 4).

a(n) = A014681(A163537(n)).

Name corrected by Kevin Ryde, Aug 29 2020

A163532 The change in X-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.

Original entry on oeis.org

0, 1, 1, 0, -1, -1, 0, 1, 1, 1, 1, 1, 0, -1, -1, 0, 1, 1, 1, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 1, 1, 1, 0, -1, -1, 0, 1, 1, 1, 1, 1, 0, -1, -1, 0, 1, 1, 1, 1, 1, 0, -1, -1, 0

Offset: 0

Antti Karttunen, Aug 01 2009

sign

Antti Karttunen, Table of n, a(n) for n = 0..59049

A014578(n) = |a(n)|. These are the first differences of A163528. See also: A163533, A163534, A163536.

a(0)=0, a(n) = A163528(n) - A163528(n-1).

Name corrected by Kevin Ryde, Aug 28 2020

A163533 The change in Y-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0

Offset: 0

Antti Karttunen, Aug 01 2009

sign

Antti Karttunen, Table of n, a(n) for n = 0..59049

These are the first differences of A163529. See also: A163532, A163534, A163536.

a(0)=0, a(n) = A163529(n) - A163529(n-1).

Name corrected by Kevin Ryde, Aug 29 2020

A166041 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163357 as where n is located in the array A163334.

Original entry on oeis.org

0, 1, 14, 13, 2, 3, 4, 7, 8, 11, 30, 29, 18, 17, 12, 15, 16, 19, 20, 21, 234, 233, 22, 23, 24, 25, 230, 229, 26, 27, 36, 37, 218, 217, 38, 39, 34, 33, 52, 53, 32, 35, 28, 31, 10, 9, 6, 5, 58, 57, 54, 55, 56, 59, 60, 61, 50, 49, 62, 63, 64, 67, 68, 69, 122, 123, 44, 47, 48

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Fixed points are quite rare: A165465.

			The top left 9 X 9 corner of A163334:
   0  1  2 15 16 17 18 19 20
   5  4  3 14 13 12 23 22 21
   6  7  8  9 10 11 24 25 26
  47 46 45 44 43 42 29 28 27
  48 49 50 39 40 41 30 31 32
  53 52 51 38 37 36 35 34 33
  54 55 56 69 70 71 72 73 74
  59 58 57 68 67 66 77 76 75
  60 61 62 63 64 65 78 79 80
The top left 8 X 8 corner of A163357:
   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
9 is in position (2,3) in A163334, while A163357(2,3) = 11. Thus a(9) = 11.

Inverse: A166042. a(n) = A163357(A163335(n)) = A163359(A163337(n)). Cf. also A166043.

A163480 Row 0 of A163334 (column 0 of A163336).

Original entry on oeis.org

0, 1, 2, 15, 16, 17, 18, 19, 20, 141, 142, 143, 144, 145, 146, 159, 160, 161, 162, 163, 164, 177, 178, 179, 180, 181, 182, 1275, 1276, 1277, 1278, 1279, 1280, 1293, 1294, 1295, 1296, 1297, 1298, 1311, 1312, 1313, 1314, 1315, 1316, 1437, 1438, 1439

Offset: 0

Antti Karttunen, Jul 29 2009

nonn

Cf. A163481 (Y axis), A037314 (Z-order X axis).

Coordinates: A163528, A163529.

a(n) = my(v=digits(n,3),s=Mod(0,2)); for(i=1,#v, if(s,v[i]+=6); s+=v[i]); fromdigits(v,9); \\ Kevin Ryde, Sep 29 2020

a(n) = A163332(A037314(n)). - Kevin Ryde, Sep 29 2020

cp's OEIS Frontend

A163528 The X-coordinate of the n-th point in the Peano curve A163334.

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A163529 The Y-coordinate of the n-th point in the Peano curve A163334.

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A163335 Inverse permutation to A163334.

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A163531 The square of the distance from the origin to the n-th point in the Peano curve A163334.

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A163534 The absolute direction (0=east, 1=south, 2=west, 3=north) of the Peano curve A163334 at point n.

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A163536 The relative direction (0=straight ahead, 1=turn right, 2=turn left) of the Peano curve A163334 at point n.

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A163532 The change in X-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.

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A163533 The change in Y-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.

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A166041 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163357 as where n is located in the array A163334.

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