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%I #16 Jul 09 2022 12:14:17
%S 0,2,1,6,8,5,3,7,4,17,20,11,24,26,18,15,23,9,14,19,10,21,25,16,12,22,
%T 13,35,53,29,56,62,47,33,51,27,60,74,54,78,80,71,59,72,44,45,61,32,65,
%U 77,50,34,52,28,38,55,30,57,69,42,36,46,31,63,73,48,75,79
%N Lexigraphically earliest sequence of distinct nonnegative integers such that for any n >= 0, among the ternary digits of n and a(n) (counted with multiplicity) there are as many 1's as 2's.
%C This sequence is a self-inverse permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A352760/b352760.txt">Table of n, a(n) for n = 0..6560</a>
%H Rémy Sigrist, <a href="/A352760/a352760.gp.txt">PARI program</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = n iff n belongs to A039001.
%F a(n) < 3^k iff n < 3^k.
%e The first terms, alongside their ternary expansions, are:
%e n a(n) ter(n) ter(a(n))
%e -- ---- ------ ---------
%e 0 0 0 0
%e 1 2 1 2
%e 2 1 2 1
%e 3 6 10 20
%e 4 8 11 22
%e 5 5 12 12
%e 6 3 20 10
%e 7 7 21 21
%e 8 4 22 11
%e 9 17 100 122
%e 10 20 101 202
%e 11 11 102 102
%e 12 24 110 220
%o (PARI) See Links section.
%Y Cf. A004488, A039001 (fixed points), A331275, A355504.
%K nonn,base
%O 0,2
%A _Rémy Sigrist_, Jul 05 2022