A306229 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, K(n) <> K(a(n)) (where K denotes the Kolakoski sequence A000002).

2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 13, 14, 11, 12, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 33, 35, 31, 36, 32, 34, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 53, 54, 51, 52, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 67, 68, 65

Offset

1,1

Comments

This sequence is a self-inverse permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1000

Rémy Sigrist, PARI program for A306229

Index entries for sequences that are permutations of the natural numbers

Formula

a(A013947(n)) = A013948(n).

a(A013948(n)) = A013947(n).

o(n) = o(a(n)) where o corresponds to the ordinal transform of A000002.

Example

The first terms of the sequence, alongside K and its ordinal transform, are:
  n   a(n)  K(n)  o(n)
  --  ----  ----  ----
   1     2     1     1
   2     1     2     1
   3     4     2     2
   4     3     1     2
   5     6     1     3
   6     5     2     3
   7     8     1     4
   8     7     2     4
   9    10     2     5
  10     9     1     5
  11    13     2     6
  12    14     2     7
  13    11     1     6
  14    12     1     7
  15    16     2     8
  16    15     1     8
  17    18     1     9
  18    17     2     9
  19    20     2    10
  20    19     1    10

Prog

(PARI) See Links section.

Crossrefs

See A306230 for a similar sequence.

Cf. A000002, A013947, A013948.

Sequence in context: A103889 A137805 A163501 * A096779 A243500 A026262

Adjacent sequences: A306226 A306227 A306228 * A306230 A306231 A306232

Keyword

nonn

Author

Rémy Sigrist, Jan 30 2019

Status

approved