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%I #12 Mar 01 2021 02:12:41
%S 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 18,27,17,23,16,31,62,60,58,56,57,52,50,54,53,49,44,51,42,48,46,61,45,
%U 41,38,43,37,40,39,59,35,36,34,55,33,47,32,63,126,124,122
%N Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, {A000120(n), A080791(n)} = {A000120(a(n)), A080791(a(n))}
%C This sequence is a self-inverse permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A342102/b342102.txt">Table of n, a(n) for n = 0..8191</a>
%H 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 Rémy Sigrist, <a href="/A342102/a342102.gp.txt">PARI program for A342102</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(2^k-1) = 2^k-1 for any k >= 0.
%F a(n) < 2^k for any n < 2^k.
%e The first terms, in decimal and in binary, alongside {A000120(n), A080791(n)}, are:
%e n a(n) bin(n) bin(a(n)) {A000120(n), A080791(n)}
%e -- ---- ------ --------- ------------------------
%e 0 0 0 0 {0}
%e 1 1 1 1 {0, 1}
%e 2 2 10 10 {1}
%e 3 3 11 11 {0, 2}
%e 4 6 100 110 {1, 2}
%e 5 5 101 101 {1, 2}
%e 6 4 110 100 {1, 2}
%e 7 7 111 111 {0, 3}
%e 8 14 1000 1110 {1, 3}
%e 9 12 1001 1100 {2}
%e 10 10 1010 1010 {2}
%e 11 13 1011 1101 {1, 3}
%e 12 9 1100 1001 {2}
%e 13 11 1101 1011 {1, 3}
%e 14 8 1110 1000 {1, 3}
%e 15 15 1111 1111 {0, 4}
%o (PARI) See Links section.
%Y See A342115, A342116 and A342117 for similar sequences.
%Y Cf. A000120, A080791, A331274, A337242.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Feb 28 2021