%I #8 May 03 2022 16:51:43

%S 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 47,27,41,28,42,26,43,29,46,30,51,20,52,21,53,22,54,31,59,153,32,48,

%U 33,49,35,55,36,56,34,57,37,68,39,69,38,70,134,40,71,132,72

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

%C Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.

%C This sequence is a permutation of the nonnegative integers with inverse A353650.

%H Rémy Sigrist, <a href="/A353649/b353649.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms, in decimal and in balanced ternary, are:

%e n a(n) bter(a(n))

%e -- ---- ----------

%e 0 0 0

%e 1 1 1

%e 2 2 1T

%e 3 6 1T0

%e 4 3 10

%e 5 5 1TT

%e 6 4 11

%e 7 8 10T

%e 8 15 1TT0

%e 9 9 100

%e 10 14 1TTT

%e 11 10 101

%e 12 17 1T0T

%e 13 7 1T1

%e 14 18 1T00

%o (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 { 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 Cf. A059095, A109812 (binary analog), A353648, A353650 (inverse).

%K nonn,look,base

%O 0,3

%A _Rémy Sigrist_, May 01 2022