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A166044 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.

%I A166044 #6 Oct 27 2019 22:22:56
%S A166044 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 A166044 68,69,38,51,50,39,40,41,36,37,70,67,66,71,72,77,76,73,34,35,30,31,28,
%U A166044 25,24,29,42,43,10,11,12,13,16,17,18,23,22,19,20,141,140,21,26,27,134
%N A166044 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 A166044 A. Karttunen, <a href="/A166044/b166044.txt">Table of n, a(n) for n = 0..16383</a>
%H A166044 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A166044 The top left 8 X 8 corner of A163357:
%e A166044    0  1 14 15 16 19 20 21
%e A166044    3  2 13 12 17 18 23 22
%e A166044    4  7  8 11 30 29 24 25
%e A166044    5  6  9 10 31 28 27 26
%e A166044   58 57 54 53 32 35 36 37
%e A166044   59 56 55 52 33 34 39 38
%e A166044   60 61 50 51 46 45 40 41
%e A166044   63 62 49 48 47 44 43 42
%e A166044 The top left 9 X 9 corner of A163336:
%e A166044    0  5  6 47 48 53 54 59 60
%e A166044    1  4  7 46 49 52 55 58 61
%e A166044    2  3  8 45 50 51 56 57 62
%e A166044   15 14  9 44 39 38 69 68 63
%e A166044   16 13 10 43 40 37 70 67 64
%e A166044   17 12 11 42 41 36 71 66 65
%e A166044   18 23 24 29 30 35 72 77 78
%e A166044   19 22 25 28 31 34 73 76 79
%e A166044   20 21 26 27 32 33 74 75 80
%e A166044 12 is in position (1,3) in A163357, while A163336(1,3) = 46. Thus a(12) = 46.
%Y A166044 Inverse: A166043. a(n) = A163336(A163358(n)) = A163334(A163360(n)). Fixed points: A165467. Cf. also A166042.
%K A166044 nonn
%O A166044 0,2
%A A166044 _Antti Karttunen_, Oct 06 2009