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A368316 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and Sum_{k = 0..n-1} a(k) can be added without carries in balanced ternary.

%I A368316 #9 Dec 24 2023 09:37:20
%S A368316 0,1,2,5,3,15,4,6,41,9,18,10,125,12,16,8,45,13,14,369,27,54,28,11,7,
%T A368316 126,17,55,26,1107,30,51,31,131,36,46,29,375,37,44,39,123,40,42,35,
%U A368316 3285,57,24,135,81,405,82,38,19,132,53,1134,84,25,134,85,23,378
%N A368316 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and Sum_{k = 0..n-1} a(k) can be added without carries in balanced ternary.
%C A368316 Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.
%C A368316 If we restrict ourselves to positive integers and allow duplicates, then we obtain A236313.
%C A368316 This sequence can be seen as a variant of A278742; however, the present sequence is not strictly increasing.
%C A368316 Will every nonnegative integer appear in the sequence?
%H A368316 Rémy Sigrist, <a href="/A368316/a368316.gp.txt">PARI program</a>
%H A368316 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%e A368316 The first terms, alongside the balanced ternary expansions of a(n) and b(n) = Sum_{k = 0..n-1} a(k), are:
%e A368316   n           |  0  1   2    3    4     5     6     7      8      9     10
%e A368316   a(n)        |  0  1   2    5    3    15     4     6     41      9     18
%e A368316   bter(b(n))  |  0  0   1   10  10T   11T  100T  1010   1100  100TT  101TT
%e A368316   bter(a(n))  |  0  1  1T  1TT   10  1TT0    11   1T0  1TTTT    100   1T00
%o A368316 (PARI) See Links section.
%Y A368316 Cf. A236313, A278742.
%K A368316 nonn,base
%O A368316 0,3
%A A368316 _Rémy Sigrist_, Dec 21 2023