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%I #15 Sep 06 2017 21:21:37
%S 1,3,2,7,6,4,5,14,15,13,12,9,8,10,11,28,29,31,30,27,26,24,25,18,19,17,
%T 16,21,20,22,23,56,57,59,58,63,62,60,61,54,55,53,52,49,48,50,51,36,37,
%U 39,38,35,34,32,33,42,43,41,40,45,44,46,47,112,113,115,114,119,118,116
%N A permutation of the natural numbers where a(n) = n XOR [n/2] XOR [n/4].
%C Related to Gray code numbers (A003188) since A003188(n) = n XOR [n/2].
%C Inverse: A100280; A100281(n) = a(a(n)). - _Reinhard Zumkeller_, Nov 11 2004
%H Ivan Neretin, <a href="/A099896/b099896.txt">Table of n, a(n) for n = 1..8191</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F XOR BINOMIAL transform begins: B={1, 2, 3, 7, 7, 0, 0, 14, 14, 0, 0, ...} and continues with B(2^k)=B(2^k+1)=7*2^(k-2) (for k>=2) and zeros elsewhere.
%t Array[BitXor[BitXor[#,Floor[#/2]],Floor[#/4]]&,70] (* _Harvey P. Dale_, Aug 10 2012 *)
%o (PARI) a(n)=bitxor(bitxor(n,n\2),n\4)
%Y Cf. A003188, A099884.
%K nonn,look
%O 1,2
%A _Paul D. Hanna_, Nov 09 2004
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