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A342102 Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, {A000120(n), A080791(n)} = {A000120(a(n)), A080791(a(n))}.

%I A342102 #17 Jun 02 2025 15:24:03
%S A342102 0,1,2,3,6,5,4,7,14,12,10,13,9,11,8,15,30,28,26,25,24,22,21,29,20,19,
%T A342102 18,27,17,23,16,31,62,60,58,56,57,52,50,54,53,49,44,51,42,48,46,61,45,
%U A342102 41,38,43,37,40,39,59,35,36,34,55,33,47,32,63,126,124,122
%N A342102 Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, {A000120(n), A080791(n)} = {A000120(a(n)), A080791(a(n))}.
%C A342102 This sequence is a self-inverse permutation of the nonnegative integers.
%H A342102 Rémy Sigrist, <a href="/A342102/b342102.txt">Table of n, a(n) for n = 0..8191</a>
%H A342102 Rémy Sigrist, <a href="/A342102/a342102.png">Colored scatterplot of the first 2^20 terms</a> (where the color is function of min(A000120(n), A080791(n)))
%H A342102 Rémy Sigrist, <a href="/A342102/a342102.gp.txt">PARI program for A342102</a>
%H A342102 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A342102 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A342102 a(2^k-1) = 2^k-1 for any k >= 0.
%F A342102 a(n) < 2^k for any n < 2^k.
%e A342102 The first terms, in decimal and in binary, alongside {A000120(n), A080791(n)}, are:
%e A342102   n   a(n)  bin(n)  bin(a(n))  {A000120(n), A080791(n)}
%e A342102   --  ----  ------  ---------  ------------------------
%e A342102    0     0       0          0  {0}
%e A342102    1     1       1          1  {0, 1}
%e A342102    2     2      10         10  {1}
%e A342102    3     3      11         11  {0, 2}
%e A342102    4     6     100        110  {1, 2}
%e A342102    5     5     101        101  {1, 2}
%e A342102    6     4     110        100  {1, 2}
%e A342102    7     7     111        111  {0, 3}
%e A342102    8    14    1000       1110  {1, 3}
%e A342102    9    12    1001       1100  {2}
%e A342102   10    10    1010       1010  {2}
%e A342102   11    13    1011       1101  {1, 3}
%e A342102   12     9    1100       1001  {2}
%e A342102   13    11    1101       1011  {1, 3}
%e A342102   14     8    1110       1000  {1, 3}
%e A342102   15    15    1111       1111  {0, 4}
%o A342102 (PARI) \\ See Links section.
%Y A342102 See A342115, A342116 and A342117 for similar sequences.
%Y A342102 Cf. A000120, A080791, A331274, A337242.
%K A342102 nonn,base
%O A342102 0,3
%A A342102 _Rémy Sigrist_, Feb 28 2021