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A357530 Reverse run lengths in binary expansions of terms of A031443: for n > 0, a(n) is the unique k such that A031443(k) = A056539(A031443(n)); a(0) = 0.

%I A357530 #10 Oct 03 2022 15:08:00
%S A357530 0,1,2,3,4,11,8,7,6,9,12,5,10,13,14,45,41,31,18,38,28,21,22,27,37,36,
%T A357530 26,23,20,29,39,17,32,42,46,35,25,24,19,30,40,16,33,43,47,15,34,44,48,
%U A357530 49,170,165,150,115,54,161,146,111,58,136,101,68,81,88,123
%N A357530 Reverse run lengths in binary expansions of terms of A031443: for n > 0, a(n) is the unique k such that A031443(k) = A056539(A031443(n)); a(0) = 0.
%C A357530 This sequence is a self-inverse permutation of the nonnegative integers.
%H A357530 Rémy Sigrist, <a href="/A357530/b357530.txt">Table of n, a(n) for n = 0..8788</a>
%H A357530 Rémy Sigrist, <a href="/A357530/a357530.gp.txt">PARI program</a>
%H A357530 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A357530 a(n) = n iff n = 0 or A031443(n) belongs to A044918.
%e A357530 For n = 42:
%e A357530 - A031443(42) = 210,
%e A357530 - the binary expansion of 210 is "11010010",
%e A357530 - reversing run lengths yields "10110100",
%e A357530 - this corresponds to 180 = A031443(33),
%e A357530 - hence a(42) = 33.
%o A357530 (PARI) See Links section.
%Y A357530 See A057164 for a similar sequence.
%Y A357530 Cf. A031443, A044918, A056539.
%K A357530 nonn,base
%O A357530 0,3
%A A357530 _Rémy Sigrist_, Oct 02 2022