A306230 -id:A306230 - cp's OEIS frontend

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

Rémy Sigrist, Jan 30 2019

nonn

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

			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

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

See A306230 for a similar sequence.

Cf. A000002, A013947, A013948.

PARI
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a(A013947(n)) = A013948(n).
a(A013948(n)) = A013947(n).
o(n) = o(a(n)) where o corresponds to the ordinal transform of A000002.

cp's OEIS Frontend

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).

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