%I #9 Oct 03 2024 11:02:33

%S 2,1,6,5,4,3,10,9,8,7,16,15,14,13,12,11,24,23,22,21,20,19,18,17,28,27,

%T 26,25,40,39,38,37,36,35,34,33,32,31,30,29,48,47,46,45,44,43,42,41,56,

%U 55,54,53,52,51,50,49,68,67,66,65,64,63,62,61,60,59,58

%N a(n) is the unique number k different from n such that the words A376637(n) and A376637(k) have the same run lengths transform.

%C Also, replacing 1's by 2's and 2's by 1's in A376637(n) yields A376637(a(n)).

%C This sequence is a self-inverse permutation of the positive integers without fixed points.

%H Rémy Sigrist, <a href="/A376674/b376674.txt">Table of n, a(n) for n = 1..10048</a>

%H Rémy Sigrist, <a href="/A376674/a376674.gp.txt">PARI program</a>

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

%F A351653(A376637(a(n))) = A351653(A376637(n)).

%e The first terms, alongside the corresponding terms from A376637 and their run lengths transform, are:

%e n a(n) A376637(n) A376637(a(n)) RL

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

%e 1 2 1 2 1

%e 2 1 2 1 1

%e 3 6 11 22 2

%e 4 5 12 21 11

%e 5 4 21 12 11

%e 6 3 22 11 2

%e 7 10 112 221 21

%e 8 9 122 211 12

%e 9 8 211 122 12

%e 10 7 221 112 21

%e 11 16 1121 2212 211

%e 12 15 1122 2211 22

%e 13 14 1211 2122 112

%e 14 13 2122 1211 112

%e 15 12 2211 1122 22

%e 16 11 2212 1121 211

%o (PARI) \\ See Links section.

%Y Cf. A351653, A376637.

%K nonn,base

%O 1,1

%A _Rémy Sigrist_, Oct 01 2024