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A353648 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) can be added without carries in balanced ternary.

%I A353648 #10 May 03 2022 17:10:34
%S A353648 0,2,1,5,6,3,4,17,15,14,18,16,19,23,9,8,11,7,10,12,51,50,53,13,44,45,
%T A353648 42,41,47,43,46,54,48,49,56,52,55,57,69,68,71,27,26,29,24,25,30,28,32,
%U A353648 33,21,20,35,22,31,36,34,37,149,153,152,155,150,151,156,154
%N A353648 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) can be added without carries in balanced ternary.
%C A353648 Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.
%C A353648 This sequence is a self-inverse permutation of the nonnegative integers with a single fixed point: a(0) = 0.
%H A353648 Rémy Sigrist, <a href="/A353648/b353648.txt">Table of n, a(n) for n = 0..10000</a>
%H A353648 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%H A353648 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A353648 The first terms, in decimal and in balanced ternary, are:
%e A353648   n         |  0   1   2    3    4    5    6     7     8     9    10    11    12
%e A353648   a(n)      |  0   2   1    5    6    3    4    17    15    14    18    16    19
%e A353648   bter(n)   |  0   1  1T   10   11  1TT  1T0   1T1   10T   100   101   11T   110
%e A353648   bter(a(n))|  0  1T   1  1TT  1T0   10   11  1T0T  1TT0  1TTT  1T00  1TT1  1T01
%o A353648 (PARI) ok(u, v) = { while (u && v, my (uu=[0, +1, -1][1+u%3], vv=[0, +1, -1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); 1 }
%o A353648 { s=0; for (n=0, 65, for (v=0, oo, if (!bittest(s,v) && ok(n,v), print1 (v", "); s+=2^v; break))) }
%Y A353648 Cf. A059095, A238757 (binary analog), A353649.
%K A353648 nonn,look,base
%O A353648 0,2
%A A353648 _Rémy Sigrist_, May 01 2022