A343312 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the digits "-1" in the balanced ternary representation of a(n) correspond to digits "+1" in that of a(n+1).

0, 1, 2, 4, 3, 5, 13, 6, 11, 7, 12, 8, 10, 9, 14, 40, 15, 38, 16, 39, 17, 34, 20, 37, 18, 32, 22, 33, 21, 35, 19, 36, 23, 31, 24, 29, 25, 30, 26, 28, 27, 41, 121, 42, 119, 43, 120, 44, 115, 47, 118, 45, 113, 49, 114, 48, 116, 46, 117, 50, 103, 59, 112, 51, 101

Offset: 0

Author

Rémy Sigrist, Apr 11 2021

Keywords

• nonn
• base
• look

Comments

This sequence is a permutation of the nonnegative integers (with inverse A343313):

- we can always extend the sequence with a member of A003462 sufficiently large,

- so the sequence is infinite and unbounded,

- once we have a k-digit number and before introducing a number with more than k digits, we must use A003462(k),

- so we have infinitely many terms of A003462 in this sequence,

- for any m with k digits, we have infinitely many terms of A003462 > m in the sequence, each of these terms can be followed by m, so m must eventually appear.

Apparently:

- the sequence preserves the number of digits in balanced ternary representation (A134021),

- fixed points correspond to 0 and A007051.

Examples

			The first terms, alongside their balanced ternary representation (with "T" instead of digits "-1"), are:
  n   a(n)  bter(a(a))
  --  ----  ----------
   0     0           0
   1     1           1
   2     2          1T
   3     4          11
   4     3          10
   5     5         1TT
   6    13         111
   7     6         1T0
   8    11         11T
   9     7         1T1
  10    12         110
  11     8         10T
  12    10         101
  13     9         100
  14    14        1TTT
  15    40        1111
  16    15        1TT0
  17    38        111T
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..9842
• Rémy Sigrist, Scatterplot of the sequence for n = 0..3^9
• Rémy Sigrist, PARI program for A343312
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A003462, A007051, A134021, A343228, A343229, A343313 (inverse).

Programs

PARI

See Links section.

Formula

A343229(a(n)) AND A343228(a(n+1)) = A343228(a(n+1)) (where AND denotes the bitwise AND operator).