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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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%I #6 Oct 27 2019 22:22:07

%S 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,

%T 28,29,42,11,10,43,40,37,36,41,30,31,34,35,72,73,76,77,66,71,70,67,68,

%U 57,56,69,38,39,50,51,52,49,48,53,54,55,58,59,60,425,424,61,62,63,422

%N 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.

%H A. Karttunen, <a href="/A166042/b166042.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 A163334:

%e 0 1 2 15 16 17 18 19 20

%e 5 4 3 14 13 12 23 22 21

%e 6 7 8 9 10 11 24 25 26

%e 47 46 45 44 43 42 29 28 27

%e 48 49 50 39 40 41 30 31 32

%e 53 52 51 38 37 36 35 34 33

%e 54 55 56 69 70 71 72 73 74

%e 59 58 57 68 67 66 77 76 75

%e 60 61 62 63 64 65 78 79 80

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

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

%K nonn

%O 0,3

%A _Antti Karttunen_, Oct 06 2009