A343766 Lexicographically earliest sequence of distinct integers such that a(0) = 0 and the balanced ternary expansions of two consecutive terms differ by a single digit, as far to the right as possible.

0, -1, 1, -2, -4, -3, 3, 2, 4, -5, -7, -6, -12, -13, -11, -8, -10, -9, 9, 8, 10, 7, 5, 6, 12, 11, 13, -14, -16, -15, -21, -22, -20, -17, -19, -18, -36, -37, -35, -38, -40, -39, -33, -34, -32, -23, -25, -24, -30, -31, -29, -26, -28, -27, 27, 26, 28, 25, 23, 24

Offset: 0

Author

Rémy Sigrist, Apr 28 2021

Keywords

• sign
• base

Comments

This sequence has similarities with A003188 and with A341055.

A007949 gives the positions of the digit that is altered from one term to the other.

To compute a(n):

- consider the ternary representation of A128173(n),

- replace 1's by -1's and 2's by 1's,

- convert back to decimal.

Examples

			The first terms, alongside their balanced ternary expansion (with T's denoting -1's), are:
  n   a(n)  bter(a(n))
  --  ----  ----------
   0     0           0
   1    -1           T
   2     1           1
   3    -2          T1
   4    -4          TT
   5    -3          T0
   6     3          10
   7     2          1T
   8     4          11
   9    -5         T11
  10    -7         T1T
  11    -6         T10
  12   -12         TT0
  13   -13         TTT
  14   -11         TT1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560
• Rémy Sigrist, Scatterplot of the first 3^10 terms
• Rémy Sigrist, PARi program for A343766
• Index entries for sequences that are permutations of the integers

Crossrefs

Cf. A003188, A007949, A024023, A081134, A128173, A341055.

Programs

PARI

See Links section.

Formula

a(n) = -A117966(A128173(n)).

Sum_{k=0..n-1} sign(a(k)) = -A081134(n).

Sum_{k=0..n} a(k) = 0 iff n belongs to A024023.