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A357527 Reverse run lengths in binary expansions of terms of A044813: for n > 0, a(n) is the unique k such that A044813(k) = A056539(A044813(n)); a(0) = 0.

%I A357527 #12 Oct 03 2022 14:56:04
%S A357527 0,1,2,4,3,5,7,6,8,12,11,10,9,13,23,18,20,22,15,21,16,19,17,14,24,36,
%T A357527 29,33,35,26,34,32,31,27,30,28,25,37,55,44,47,49,52,54,39,53,51,40,50,
%U A357527 41,48,46,42,45,43,38,56,82,63,68,76,79,81,58,69,73,80,78
%N A357527 Reverse run lengths in binary expansions of terms of A044813: for n > 0, a(n) is the unique k such that A044813(k) = A056539(A044813(n)); a(0) = 0.
%C A357527 This sequence is a self-inverse permutation of the nonnegative integers.
%H A357527 Rémy Sigrist, <a href="/A357527/b357527.txt">Table of n, a(n) for n = 0..11666</a>
%H A357527 Rémy Sigrist, <a href="/A357527/a357527.gp.txt">PARI program</a>
%H A357527 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A357527 a(n) = n iff n = 0 or A044813(n) belongs to A044918.
%e A357527 For n = 42:
%e A357527 - A044813(42) = 159,
%e A357527 - the binary expansion of 159 is "10011111",
%e A357527 - reversing run lengths yields "11111001",
%e A357527 - this corresponds to 249 = A044813(52),
%e A357527 - hence a(42) = 52.
%o A357527 (PARI) See Links section.
%Y A357527 See A057164, A357522 and A357523 for similar sequences.
%Y A357527 Cf. A044813, A044918, A056539.
%K A357527 nonn,look,base
%O A357527 0,3
%A A357527 _Rémy Sigrist_, Oct 02 2022