A306230 -id:A306230

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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).

+10
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.

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jan 30 2019

STATUS

approved

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