%N If the rightmost block of zeros in binary representation of n has an even length, then delete one 0, otherwise insert one 0 in this block.
%C a(a(n))=n, self-inverse permutation of natural numbers;
%C a(n) = n iff n = 2^k - 1, k>0;
%C -1<=A023416(a(n))-A023416(n)<=1; A000120(a(n))=A000120(n); -1<=A070939(a(n))-A070939(n)<=1.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(2n+1) = 2a(n)+1, a(4n+2) = 8n+4, a(4n) = 2n(4-3*A035263(n)). - _Ralf Stephan_, Oct 09 2003
%e n=43 in binary 101011: insert a 0 in the rightmost block of zeros
%e consisting of one (odd!) 0: 1010011 -> 83=a(43);
%e n=41 in binary 101001: delete a 0 from the rightmost block of
%e zeros consisting of two (even!) 0's: 10101 -> 21=a(41).
%Y Cf. A084484(n)=A007088(a(n)).
%A _Reinhard Zumkeller_, May 27 2003