A163336 -id:A163336 - cp's OEIS frontend

A165466 Squared distance between n's location in A163334 array and A163359 array.

0, 2, 2, 2, 2, 10, 10, 2, 0, 0, 2, 10, 20, 10, 10, 18, 32, 32, 50, 74, 100, 100, 72, 50, 32, 50, 50, 34, 20, 20, 16, 16, 16, 10, 4, 4, 2, 4, 8, 8, 8, 10, 20, 18, 20, 20, 26, 50, 50, 40, 20, 20, 20, 20, 32, 32, 34, 40, 58, 74, 100, 74, 74, 80, 80, 80, 52, 52, 50, 34, 34, 32

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Equivalently, squared distance between n's location in A163336 array and A163357 array. See example at A166043.

A. Karttunen, Table of n, a(n) for n = 0..65535

Positions of zeros: A165467. See also A166043, A165464, A163897, A163900.

a(n) = A000290(abs(A163529(n)-A059253(n))) + A000290(abs(A163528(n)-A059252(n))).

A166042 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163334 as where n is located in the array A163357.

Original entry on oeis.org

0, 1, 4, 5, 6, 47, 46, 7, 8, 45, 44, 9, 14, 3, 2, 15, 16, 13, 12, 17, 18, 19, 22, 23, 24, 25, 28, 29, 42, 11, 10, 43, 40, 37, 36, 41, 30, 31, 34, 35, 72, 73, 76, 77, 66, 71, 70, 67, 68, 57, 56, 69, 38, 39, 50, 51, 52, 49, 48, 53, 54, 55, 58, 59, 60, 425, 424, 61, 62, 63, 422

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

			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
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
9 is in position (3,2) in A163357, while A163334(3,2) = 45. Thus a(9) = 45.

Inverse: A166041. a(n) = A163334(A163358(n)) = A163336(A163360(n)). Fixed points: A165465. Cf. also A166044.

A163333 Self-inverse permutation of integers: A163327-conjugate of A163332.

Original entry on oeis.org

0, 7, 2, 3, 4, 5, 6, 1, 8, 69, 64, 71, 66, 67, 68, 63, 70, 65, 18, 25, 20, 21, 22, 23, 24, 19, 26, 29, 34, 27, 32, 31, 30, 35, 28, 33, 44, 37, 42, 41, 40, 39, 38, 43, 36, 47, 52, 45, 50, 49, 48, 53, 46, 51, 54, 61, 56, 57, 58, 59, 60, 55, 62, 15, 10, 17, 12, 13, 14, 9, 16, 11

Offset: 0

Antti Karttunen, Jul 29 2009

nonn

The integers [0,(9^k)-1] are confined to range [0,(9^k)-1].

a(n) = A163327(A163332(A163327(n))). A163334 & A163336 give two variants of the Peano curve in an N x N grid. Cf. also A163355.

A165464 Squared distance between n's location in A163334 array and A163357 array.

Original entry on oeis.org

0, 0, 2, 4, 2, 4, 2, 0, 0, 2, 2, 4, 4, 4, 2, 0, 0, 2, 2, 4, 4, 2, 0, 0, 0, 0, 2, 4, 4, 2, 8, 10, 16, 16, 4, 2, 2, 10, 16, 10, 8, 8, 20, 20, 20, 18, 18, 32, 18, 10, 4, 2, 4, 10, 8, 2, 2, 10, 10, 4, 4, 4, 2, 10, 16, 26, 20, 10, 2, 4, 10, 18, 32, 32, 50, 52, 52, 34, 40, 58, 80, 80, 106, 146

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Equivalently, squared distance between n's location in A163336 array and A163359 array. See example at A166041.

A. Karttunen, Table of n, a(n) for n = 0..65535

Positions of zeros: A165465. See also A165466, A163897, A163900.

a(n) = A000290(abs(A163529(n)-A059252(n))) + A000290(abs(A163528(n)-A059253(n))).

cp's OEIS Frontend

A165466 Squared distance between n's location in A163334 array and A163359 array.

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A166042 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163334 as where n is located in the array A163357.

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A163333 Self-inverse permutation of integers: A163327-conjugate of A163332.

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A165464 Squared distance between n's location in A163334 array and A163357 array.

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