A306229 - OEIS

%I #18 Feb 11 2019 20:56:45

%S 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,

%T 28,27,30,29,33,35,31,36,32,34,38,37,40,39,42,41,44,43,46,45,48,47,50,

%U 49,53,54,51,52,56,55,58,57,60,59,62,61,64,63,67,68,65

%N 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).

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

%H Rémy Sigrist, <a href="/A306229/b306229.txt">Table of n, a(n) for n = 1..1000</a>

%H Rémy Sigrist, <a href="/A306229/a306229.gp.txt">PARI program for A306229</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

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

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

%e The first terms of the sequence, alongside K and its ordinal transform, are:

%e   n   a(n)  K(n)  o(n)

%e   --  ----  ----  ----

%e    1     2     1     1

%e    2     1     2     1

%e    3     4     2     2

%e    4     3     1     2

%e    5     6     1     3

%e    6     5     2     3

%e    7     8     1     4

%e    8     7     2     4

%e    9    10     2     5

%e   10     9     1     5

%e   11    13     2     6

%e   12    14     2     7

%e   13    11     1     6

%e   14    12     1     7

%e   15    16     2     8

%e   16    15     1     8

%e   17    18     1     9

%e   18    17     2     9

%e   19    20     2    10

%e   20    19     1    10

%o (PARI) See Links section.

%Y See A306230 for a similar sequence.

%Y Cf. A000002, A013947, A013948.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Jan 30 2019