%I #6 Oct 27 2019 22:22:56

%S 0,5,4,1,2,15,14,3,8,9,44,45,46,7,6,47,48,49,52,53,54,59,58,55,56,57,

%T 68,69,38,51,50,39,40,41,36,37,70,67,66,71,72,77,76,73,34,35,30,31,28,

%U 25,24,29,42,43,10,11,12,13,16,17,18,23,22,19,20,141,140,21,26,27,134

%N Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163336 as where n is located in the array A163357.

%H A. Karttunen, <a href="/A166044/b166044.txt">Table of n, a(n) for n = 0..16383</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The top left 8 X 8 corner of A163357:

%e 0 1 14 15 16 19 20 21

%e 3 2 13 12 17 18 23 22

%e 4 7 8 11 30 29 24 25

%e 5 6 9 10 31 28 27 26

%e 58 57 54 53 32 35 36 37

%e 59 56 55 52 33 34 39 38

%e 60 61 50 51 46 45 40 41

%e 63 62 49 48 47 44 43 42

%e The top left 9 X 9 corner of A163336:

%e 0 5 6 47 48 53 54 59 60

%e 1 4 7 46 49 52 55 58 61

%e 2 3 8 45 50 51 56 57 62

%e 15 14 9 44 39 38 69 68 63

%e 16 13 10 43 40 37 70 67 64

%e 17 12 11 42 41 36 71 66 65

%e 18 23 24 29 30 35 72 77 78

%e 19 22 25 28 31 34 73 76 79

%e 20 21 26 27 32 33 74 75 80

%e 12 is in position (1,3) in A163357, while A163336(1,3) = 46. Thus a(12) = 46.

%Y Inverse: A166043. a(n) = A163336(A163358(n)) = A163334(A163360(n)). Fixed points: A165467. Cf. also A166042.

%K nonn

%O 0,2

%A _Antti Karttunen_, Oct 06 2009