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A357523 Reverse run lengths in binary expansions of terms of A166535: for n > 0, a(n) is the unique k such that A166535(k) = A056539(A166535(n)); a(0) = 0.

%I A357523 #9 Oct 03 2022 15:07:54
%S A357523 0,1,2,3,6,5,4,7,14,9,10,13,12,11,8,15,20,23,24,19,16,27,26,17,18,25,
%T A357523 22,21,40,41,46,35,32,49,50,31,36,45,42,39,28,29,38,43,44,37,30,51,48,
%U A357523 33,34,47,88,63,62,89,94,57,68,83,80,71,54,53,72,79,84,67
%N A357523 Reverse run lengths in binary expansions of terms of A166535: for n > 0, a(n) is the unique k such that A166535(k) = A056539(A166535(n)); a(0) = 0.
%C A357523 This sequence is a self-inverse permutation of the nonnegative integers.
%H A357523 Rémy Sigrist, <a href="/A357523/b357523.txt">Table of n, a(n) for n = 0..12639</a>
%H A357523 Rémy Sigrist, <a href="/A357523/a357523.gp.txt">PARI program</a>
%H A357523 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A357523 a(n) = n iff n = 0 or A166535(n) belongs to A044918.
%e A357523 For n = 42:
%e A357523 - A166535(42) = 50,
%e A357523 - the binary expansion of 50 is "110010",
%e A357523 - reversing run lengths yields "101100",
%e A357523 - this corresponds to 44 = A166535(38),
%e A357523 - hence a(42) = 38.
%o A357523 (PARI) See Links section.
%Y A357523 See A357522 for a similar sequence.
%Y A357523 Cf. A044918, A056539, A166535.
%K A357523 nonn,base
%O A357523 0,3
%A A357523 _Rémy Sigrist_, Oct 02 2022