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

0,3

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