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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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position. This sequence is a permutation of the nonnegative integers with inverse A353650. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..10000 Wikipedia, Balanced ternary Index entries for sequences that are permutations of the natural numbers EXAMPLE 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 PROG (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))) } CROSSREFS Cf. A059095, A109812 (binary analog), A353648, A353650 (inverse). Sequence in context: A351496 A154048 A259018 * A084355 A093650 A064433 Adjacent sequences: A353646 A353647 A353648 * A353650 A353651 A353652 KEYWORD nonn,look,base AUTHOR Rémy Sigrist, May 01 2022 STATUS approved

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Last modified July 25 05:51 EDT 2024. Contains 374586 sequences. (Running on oeis4.)