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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
OFFSET
1,1
COMMENTS
This sequence is a self-inverse permutation 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.
Sequence in context: A103889 A137805 A163501 * A375757 A096779 A243500
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 30 2019
STATUS
approved