A368316 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and Sum_{k = 0..n-1} a(k) can be added without carries in balanced ternary.

0, 1, 2, 5, 3, 15, 4, 6, 41, 9, 18, 10, 125, 12, 16, 8, 45, 13, 14, 369, 27, 54, 28, 11, 7, 126, 17, 55, 26, 1107, 30, 51, 31, 131, 36, 46, 29, 375, 37, 44, 39, 123, 40, 42, 35, 3285, 57, 24, 135, 81, 405, 82, 38, 19, 132, 53, 1134, 84, 25, 134, 85, 23, 378

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.

If we restrict ourselves to positive integers and allow duplicates, then we obtain A236313.

This sequence can be seen as a variant of A278742; however, the present sequence is not strictly increasing.

Will every nonnegative integer appear in the sequence?

Links

Table of n, a(n) for n=0..62.

Rémy Sigrist, PARI program

Wikipedia, Balanced ternary

Example

The first terms, alongside the balanced ternary expansions of a(n) and b(n) = Sum_{k = 0..n-1} a(k), are:
  n           |  0  1   2    3    4     5     6     7      8      9     10
  a(n)        |  0  1   2    5    3    15     4     6     41      9     18
  bter(b(n))  |  0  0   1   10  10T   11T  100T  1010   1100  100TT  101TT
  bter(a(n))  |  0  1  1T  1TT   10  1TT0    11   1T0  1TTTT    100   1T00

Prog

(PARI) See Links section.

Crossrefs

Cf. A236313, A278742.

Sequence in context: A285742 A245612 A243066 * A181921 A282575 A002565

Adjacent sequences: A368313 A368314 A368315 * A368317 A368318 A368319

Keyword

nonn,base

Author

Rémy Sigrist, Dec 21 2023

Status

approved