A353648 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) can be added without carries in balanced ternary.

0, 2, 1, 5, 6, 3, 4, 17, 15, 14, 18, 16, 19, 23, 9, 8, 11, 7, 10, 12, 51, 50, 53, 13, 44, 45, 42, 41, 47, 43, 46, 54, 48, 49, 56, 52, 55, 57, 69, 68, 71, 27, 26, 29, 24, 25, 30, 28, 32, 33, 21, 20, 35, 22, 31, 36, 34, 37, 149, 153, 152, 155, 150, 151, 156, 154

Offset: 0

Author

Rémy Sigrist, May 01 2022

Keywords

• nonn
• look
• base

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 self-inverse permutation of the nonnegative integers with a single fixed point: a(0) = 0.

Examples

			The first terms, in decimal and in balanced ternary, are:
  n         |  0   1   2    3    4    5    6     7     8     9    10    11    12
  a(n)      |  0   2   1    5    6    3    4    17    15    14    18    16    19
  bter(n)   |  0   1  1T   10   11  1TT  1T0   1T1   10T   100   101   11T   110
  bter(a(n))|  0  1T   1  1TT  1T0   10   11  1T0T  1TT0  1TTT  1T00  1TT1  1T01
		

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

Crossrefs

Cf. A059095, A238757 (binary analog), A353649.

Programs

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; for (n=0, 65, for (v=0, oo, if (!bittest(s,v) && ok(n,v), print1 (v", "); s+=2^v; break))) }