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A266151 Take the binary representation of n, increase each run of 1's by one 1 if the length of run is odd, otherwise, if length of run is even, remove one 1. a(n) is the decimal equivalent of the result.

%I A266151 #12 Jan 20 2019 23:19:02
%S A266151 0,3,6,1,12,27,2,15,24,51,54,13,4,11,30,7,48,99,102,25,108,219,26,111,
%T A266151 8,19,22,5,60,123,14,63,96,195,198,49,204,411,50,207,216,435,438,109,
%U A266151 52,107,222,55,16,35,38,9,44,91,10,47,120,243,246,61,28,59,126,31
%N A266151 Take the binary representation of n, increase each run of 1's by one 1 if the length of run is odd, otherwise, if length of run is even, remove one 1. a(n) is the decimal equivalent of the result.
%C A266151 This is a self-inverse permutation of the positive integers.
%H A266151 Rémy Sigrist, <a href="/A266151/b266151.txt">Table of n, a(n) for n = 0..8192</a>
%H A266151 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A266151 a(4) = 12 since 4 = 100 binary -> 1100 = 12 decimal,
%e A266151 a(5) = 27 since 5 = 101 binary -> 110011 = 27 decimal,
%e A266151 a(6) = 2 since 6 = 110 binary -> 10 = 2 decimal.
%t A266151 Table[FromDigits[#, 2] &@ Flatten[If[First@ # == 1, If[OddQ@ Length@ #, Append[IntegerDigits@ #, 1], Most@ IntegerDigits@ #], #] & /@ Split@ IntegerDigits[n, 2]], {n, 63}] (* _Michael De Vlieger_, Dec 22 2015 *)
%o A266151 (PARI) a(n) = if (n==0, 0, my (b=n%2, r=valuation(n+b, 2), rr=if (b==0, r, r%2, r+1, r-1)); (a(n\2^r)+b)*2^rr-b) \\ _Rémy Sigrist_, Jan 20 2019
%Y A266151 Cf. A007088, A084483, A162853, A175046, A175047, A175048, A266150.
%K A266151 nonn,base
%O A266151 0,2
%A A266151 _Alex Ratushnyak_, Dec 21 2015
%E A266151 a(0) = 0 prepended by _Rémy Sigrist_, Jan 20 2019