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A361146 a(n) is the sibling of n in the infinite binary tree underlying A361144.

%I A361146 #11 Mar 07 2023 07:42:19
%S A361146 2,1,9,5,4,7,6,10,3,8,14,31,18,11,17,19,15,13,16,21,20,23,22,26,32,24,
%T A361146 28,27,30,29,12,25,34,33,41,37,36,39,38,42,35,40,133,46,50,44,49,51,
%U A361146 47,45,48,53,52,56,59,54,76,60,55,58,62,61,64,63,66,65,73
%N A361146 a(n) is the sibling of n in the infinite binary tree underlying A361144.
%C A361146 This sequence is a self-inverse permutation of the positive integers with no fixed point.
%H A361146 Rémy Sigrist, <a href="/A361146/a361146.gp.txt">PARI program</a>
%H A361146 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A361146 a(A361144(2*n)) = A361144(2*n-1).
%F A361146 a(A361144(2*n-1)) = A361144(2*n).
%e A361146 The infinite binary tree underlying A361144 starts as follows:
%e A361146                                 176
%e A361146                  ---------------------------------
%e A361146                 43                              133
%e A361146          -----------------               -----------------
%e A361146         12              31              57              76
%e A361146      ---------       ---------       ---------       ---------
%e A361146      3       9      13      18      25      32      35      41
%e A361146    -----   -----   -----   -----   -----   -----   -----   -----
%e A361146    1   2   4   5   6   7   8  10  11  14  15  17  16  19  20  21
%e A361146 .
%e A361146 So a(1) = 2 and a(2) = 1, a(4) = 5 and a(5) = 4, etc.,
%e A361146    a(3) = 9 and a(9) = 3, a(13) = 18 and a(18) = 13, etc.,
%e A361146    a(12) = 31 and a(31) = 12, a(57) = 76 and a(76) = 57,
%e A361146    a(43) = 133 and a(133) = 43.
%o A361146 (PARI) See Links section.
%Y A361146 Cf. A328654, A361144.
%K A361146 nonn
%O A361146 1,1
%A A361146 _Rémy Sigrist_, Mar 02 2023