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%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
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