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A166042 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.

%I A166042 #6 Oct 27 2019 22:22:07
%S A166042 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 A166042 28,29,42,11,10,43,40,37,36,41,30,31,34,35,72,73,76,77,66,71,70,67,68,
%U A166042 57,56,69,38,39,50,51,52,49,48,53,54,55,58,59,60,425,424,61,62,63,422
%N A166042 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 A166042 A. Karttunen, <a href="/A166042/b166042.txt">Table of n, a(n) for n = 0..16383</a>
%H A166042 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A166042 The top left 8 X 8 corner of A163357:
%e A166042    0  1 14 15 16 19 20 21
%e A166042    3  2 13 12 17 18 23 22
%e A166042    4  7  8 11 30 29 24 25
%e A166042    5  6  9 10 31 28 27 26
%e A166042   58 57 54 53 32 35 36 37
%e A166042   59 56 55 52 33 34 39 38
%e A166042   60 61 50 51 46 45 40 41
%e A166042   63 62 49 48 47 44 43 42
%e A166042 The top left 9 X 9 corner of A163334:
%e A166042    0  1  2 15 16 17 18 19 20
%e A166042    5  4  3 14 13 12 23 22 21
%e A166042    6  7  8  9 10 11 24 25 26
%e A166042   47 46 45 44 43 42 29 28 27
%e A166042   48 49 50 39 40 41 30 31 32
%e A166042   53 52 51 38 37 36 35 34 33
%e A166042   54 55 56 69 70 71 72 73 74
%e A166042   59 58 57 68 67 66 77 76 75
%e A166042   60 61 62 63 64 65 78 79 80
%e A166042 9 is in position (3,2) in A163357, while A163334(3,2) = 45. Thus a(9) = 45.
%Y A166042 Inverse: A166041. a(n) = A163334(A163358(n)) = A163336(A163360(n)). Fixed points: A165465. Cf. also A166044.
%K A166042 nonn
%O A166042 0,3
%A A166042 _Antti Karttunen_, Oct 06 2009