editing

approved

The top left 8x8 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 9x9 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

approved

editing

_Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), _, Oct 06 2009

<a href="/Sindx_index/Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

A. Karttunen, <a href="/A166042/b166042.txt">Table of n, a(n) for n = 0..16383</a>

<a href="/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

nonn,new

nonn

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.

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

0,3

A. Karttunen, <a href="b166042.txt">Table of n, a(n) for n = 0..16383</a>

<a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

The top left 8x8 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 9x9 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.

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 06 2009

approved