A353649 Lexicographically earliest sequence of distinct nonnegative integers such that two consecutive terms can be added without carries in balanced ternary.
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, 47, 27, 41, 28, 42, 26, 43, 29, 46, 30, 51, 20, 52, 21, 53, 22, 54, 31, 59, 153, 32, 48, 33, 49, 35, 55, 36, 56, 34, 57, 37, 68, 39, 69, 38, 70, 134, 40, 71, 132, 72
Offset: 0
Examples
The first terms, in decimal and in balanced ternary, are: n a(n) bter(a(n)) -- ---- ---------- 0 0 0 1 1 1 2 2 1T 3 6 1T0 4 3 10 5 5 1TT 6 4 11 7 8 10T 8 15 1TT0 9 9 100 10 14 1TTT 11 10 101 12 17 1T0T 13 7 1T1 14 18 1T00
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Programs
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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 } { 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))) }
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