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A355642 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the balanced ternary expansion of n * a(n) contains as many negative trits as positive trits.

%I A355642 #9 Jul 14 2022 09:34:28
%S A355642 0,2,1,6,4,12,3,8,7,16,13,14,5,10,11,26,9,24,23,28,20,22,21,18,17,32,
%T A355642 15,46,19,30,29,40,25,42,34,48,36,38,37,44,31,52,33,54,39,58,27,74,35,
%U A355642 56,55,68,41,70,43,50,49,64,45,66,60,72,63,62,57,76,59,80
%N A355642 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the balanced ternary expansion of n * a(n) contains as many negative trits as positive trits.
%C A355642 This sequence is a self-inverse permutation of the nonnegative integers.
%H A355642 Rémy Sigrist, <a href="/A355642/b355642.txt">Table of n, a(n) for n = 0..2187</a>
%H A355642 Rémy Sigrist, <a href="/A355642/a355642.gp.txt">PARI program</a>
%H A355642 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A355642 The first terms, alongside the balanced ternary expansion of n * a(n), are:
%e A355642   n   a(n)  bter(n*a(n))
%e A355642   --  ----  ------------
%e A355642    0     0             0
%e A355642    1     2            1T
%e A355642    2     1            1T
%e A355642    3     6          1T00
%e A355642    4     4          1TT1
%e A355642    5    12         1T1T0
%e A355642    6     3          1T00
%e A355642    7     8         1T01T
%e A355642    8     7         1T01T
%e A355642    9    16        1TT100
%e A355642   10    13        1TTT11
%e A355642   11    14        1T0T01
%e A355642   12     5         1T1T0
%o A355642 (PARI) See Links section.
%Y A355642 See A306993 for a similar sequence.
%Y A355642 Cf. A065363, A174658, A355639.
%K A355642 nonn,base
%O A355642 0,2
%A A355642 _Rémy Sigrist_, Jul 11 2022