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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 23 01:56 EDT 2021. Contains 345394 sequences. (Running on oeis4.)