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

0,4

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.

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

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A244646 A308182 A220080 * A299920 A352962 A137363

Adjacent sequences: A343763 A343764 A343765 * A343767 A343768 A343769

Keyword

sign,base

Author

Rémy Sigrist, Apr 28 2021

Status

approved