%I A006068 M2253
%S A006068 0,1,3,2,7,6,4,5,15,14,12,13,8,9,11,10,31,30,28,29,24,25,27,26,16,17,
%T A006068 19,18,23,22,20,21,63,62,60,61,56,57,59,58,48,49,51,50,55,54,52,53,32,
%U A006068 33,35,34,39,38,36,37,47,46,44,45,40,41,43,42,127,126,124,125,120,121
%N A006068 a(n) is Gray-coded into n.
%C A006068 Equivalently, if binary expansion of n has m bits (say), compute derivative 
               of n (A038554), getting sequence n' of length m-1; sort on n'.
%C A006068 Inverse of sequence A003188 considered as a permutation of the nonnegative 
               integers, i.e. A006068(A003188(n)) = n = A003188(A006068(n)). - Howard 
               A. Landman (howard(AT)polyamory.org), Sep 25 2001
%D A006068 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006068 M. Gardner, Mathematical Games, Sci. Amer. Vol. 227 (No. 2, Feb. 1972), 
               p. 107.
%D A006068 M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. 
               Freeman, NY, 1986, p. 15.
%H A006068 T. D. Noe, <a href="b006068.txt">Table of n, a(n) for n=0..1023</a>
%H A006068 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A006068 a(n) =2*a(ceiling[(n+1)/2])+A010060(n-1). If 3*2^(k-1) < n <= 2^(k+1), 
               a(n)=2^(k+1)-1-a(n-2^k); if 2^(k+1) < n <= 3*2^k, a(n)=a(n-2^k)+2^k.
%F A006068 a(n) = n XOR [n/2] XOR [n/4] XOR [n/8] ... XOR [n/2^m] where m = [log(n)/
               log(2)] (for n>0) and [x] is integer floor of x. - Paul D. Hanna 
               (pauldhanna(AT)juno.com), Jun 04 2002
%F A006068 A066194(n) = a(n-1) + 1, n>=1 . - Philippe DELEHAM, Apr 29 2005
%F A006068 Inverse of sequence A003188 . - Philippe DELEHAM, Apr 29 2005
%e A006068 The first few values of n' are -,-,1,0,10,11,01,00,100,101,111,110,010,
               011,001,000,... (for n=0..15) and to put these in lexicographic order 
               we must take n in the order 0,1,3,2,7,6,4,5,15,14,12,13,8,9,11,10,
               ...
%Y A006068 Cf. A038554, A005811, A003188, A014550, A003100.
%Y A006068 Sequence in context: A099896 A160679 A153141 this_sequence A154436 A072764 
               A130328
%Y A006068 Adjacent sequences: A006065 A006066 A006067 this_sequence A006069 A006070 
               A006071
%K A006068 nonn,easy,nice
%O A006068 0,3
%A A006068 N. J. A. Sloane (njas(AT)research.att.com).
%E A006068 Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), 
               Jan 10 2001