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A353649 Lexicographically earliest sequence of distinct nonnegative integers such that two consecutive terms can be added without carries in balanced ternary.

%I A353649 #8 May 03 2022 16:51:43
%S A353649 0,1,2,6,3,5,4,8,15,9,14,10,17,7,18,11,16,12,19,50,13,23,45,24,44,25,
%T A353649 47,27,41,28,42,26,43,29,46,30,51,20,52,21,53,22,54,31,59,153,32,48,
%U A353649 33,49,35,55,36,56,34,57,37,68,39,69,38,70,134,40,71,132,72
%N A353649 Lexicographically earliest sequence of distinct nonnegative integers such that two consecutive terms can be added without carries in balanced ternary.
%C A353649 Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.
%C A353649 This sequence is a permutation of the nonnegative integers with inverse A353650.
%H A353649 Rémy Sigrist, <a href="/A353649/b353649.txt">Table of n, a(n) for n = 0..10000</a>
%H A353649 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%H A353649 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A353649 The first terms, in decimal and in balanced ternary, are:
%e A353649   n   a(n)  bter(a(n))
%e A353649   --  ----  ----------
%e A353649    0     0           0
%e A353649    1     1           1
%e A353649    2     2          1T
%e A353649    3     6         1T0
%e A353649    4     3          10
%e A353649    5     5         1TT
%e A353649    6     4          11
%e A353649    7     8         10T
%e A353649    8    15        1TT0
%e A353649    9     9         100
%e A353649   10    14        1TTT
%e A353649   11    10         101
%e A353649   12    17        1T0T
%e A353649   13     7         1T1
%e A353649   14    18        1T00
%o A353649 (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 A353649 { s=0; v=0; for (n=0, 66, print1 (v", "); s+=2^v; for (w=0, oo, if (!bittest(s,w) && ok(v,w), v=w; break))) }
%Y A353649 Cf. A059095, A109812 (binary analog), A353648, A353650 (inverse).
%K A353649 nonn,look,base
%O A353649 0,3
%A A353649 _Rémy Sigrist_, May 01 2022