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A166043 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 A163336.

%I A166043 #6 Oct 27 2019 22:20:56
%S A166043 0,3,4,7,2,1,14,13,8,9,54,55,56,57,6,5,58,59,60,63,64,67,62,61,50,49,
%T A166043 68,69,48,51,46,47,122,123,44,45,34,35,28,31,32,33,52,53,10,11,12,15,
%U A166043 16,17,30,29,18,19,20,23,24,25,22,21,234,233,230,229,218,217,38,37,26
%N A166043 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 A163336.
%C A166043 Fixed points are quite rare: A165467.
%H A166043 A. Karttunen, <a href="/A166043/b166043.txt">Table of n, a(n) for n = 0..65535</a>
%H A166043 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A166043 The top left 9 X 9 corner of A163336:
%e A166043    0  5  6 47 48 53 54 59 60
%e A166043    1  4  7 46 49 52 55 58 61
%e A166043    2  3  8 45 50 51 56 57 62
%e A166043   15 14  9 44 39 38 69 68 63
%e A166043   16 13 10 43 40 37 70 67 64
%e A166043   17 12 11 42 41 36 71 66 65
%e A166043   18 23 24 29 30 35 72 77 78
%e A166043   19 22 25 28 31 34 73 76 79
%e A166043   20 21 26 27 32 33 74 75 80
%e A166043 The top left 8 X 8 corner of A163357:
%e A166043    0  1 14 15 16 19 20 21
%e A166043    3  2 13 12 17 18 23 22
%e A166043    4  7  8 11 30 29 24 25
%e A166043    5  6  9 10 31 28 27 26
%e A166043   58 57 54 53 32 35 36 37
%e A166043   59 56 55 52 33 34 39 38
%e A166043   60 61 50 51 46 45 40 41
%e A166043   63 62 49 48 47 44 43 42
%e A166043 3 is in position (2,1) in A163336, while A163357(2,1) = 7. Thus a(3) = 7.
%Y A166043 Inverse: A166044. a(n) = A163357(A163337(n)) = A163359(A163335(n)). Cf. also A166041.
%K A166043 nonn
%O A166043 0,2
%A A166043 _Antti Karttunen_, Oct 06 2009