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A166041 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 A163334.

%I A166041 #6 Oct 27 2019 21:34:42
%S A166041 0,1,14,13,2,3,4,7,8,11,30,29,18,17,12,15,16,19,20,21,234,233,22,23,
%T A166041 24,25,230,229,26,27,36,37,218,217,38,39,34,33,52,53,32,35,28,31,10,9,
%U A166041 6,5,58,57,54,55,56,59,60,61,50,49,62,63,64,67,68,69,122,123,44,47,48
%N A166041 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 A163334.
%C A166041 Fixed points are quite rare: A165465.
%H A166041 A. Karttunen, <a href="/A166041/b166041.txt">Table of n, a(n) for n = 0..65535</a>
%H A166041 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A166041 The top left 9 X 9 corner of A163334:
%e A166041    0  1  2 15 16 17 18 19 20
%e A166041    5  4  3 14 13 12 23 22 21
%e A166041    6  7  8  9 10 11 24 25 26
%e A166041   47 46 45 44 43 42 29 28 27
%e A166041   48 49 50 39 40 41 30 31 32
%e A166041   53 52 51 38 37 36 35 34 33
%e A166041   54 55 56 69 70 71 72 73 74
%e A166041   59 58 57 68 67 66 77 76 75
%e A166041   60 61 62 63 64 65 78 79 80
%e A166041 The top left 8 X 8 corner of A163357:
%e A166041    0  1 14 15 16 19 20 21
%e A166041    3  2 13 12 17 18 23 22
%e A166041    4  7  8 11 30 29 24 25
%e A166041    5  6  9 10 31 28 27 26
%e A166041   58 57 54 53 32 35 36 37
%e A166041   59 56 55 52 33 34 39 38
%e A166041   60 61 50 51 46 45 40 41
%e A166041   63 62 49 48 47 44 43 42
%e A166041 9 is in position (2,3) in A163334, while A163357(2,3) = 11. Thus a(9) = 11.
%Y A166041 Inverse: A166042. a(n) = A163357(A163335(n)) = A163359(A163337(n)). Cf. also A166043.
%K A166041 nonn
%O A166041 0,3
%A A166041 _Antti Karttunen_, Oct 06 2009