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%I #18 Jul 23 2023 01:45:29
%S 1,4,3,2,9,12,7,16,5,20,19,6,25,28,15,8,33,36,11,10,41,44,39,48,13,52,
%T 51,14,57,60,31,64,17,68,67,18,73,76,23,80,21,84,83,22,89,92,79,24,97,
%U 100,27,26,105,108,103,112,29,116,115,30,121,124,63,32,129
%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.
%H Amiram Eldar, <a href="/A084483/b084483.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F a(a(n)) = n, self-inverse permutation of natural numbers.
%F a(n) = n iff n = 2^k - 1, k>0.
%F -1 <= A023416(a(n)) - A023416(n) <= 1.
%F A000120(a(n)) = A000120(n).
%F A084484(n) = A007088(a(n)).
%F -1 <= A070939(a(n)) - A070939(n) <= 1.
%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 consisting of one (odd!) 0: 1010011 -> 83 = a(43).
%e n = 41 in binary 101001: delete a 0 from the rightmost block of zeros consisting of two (even!) 0's: 10101 -> 21 = a(41).
%t a[n_] := a[n] = If[OddQ[n], 2*a[(n - 1)/2] + 1, If[EvenQ[IntegerExponent[n, 2]], n/2, 2*n]]; Array[a, 100] (* _Amiram Eldar_, Jul 22 2023 *)
%Y Cf. A000120, A007088, A023416, A035263, A070939, A084484.
%K nonn,base
%O 1,2
%A _Reinhard Zumkeller_, May 27 2003
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