Search: id:A003188
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%I A003188 M2250
%S A003188 0,1,3,2,6,7,5,4,12,13,15,14,10,11,9,8,24,25,27,26,30,31,29,28,20,21,
%T A003188 23,22,18,19,17,16,48,49,51,50,54,55,53,52,60,61,63,62,58,59,57,56,40,
%U A003188 41,43,42,46,47,45,44,36,37,39,38,34,35,33,32,96,97,99,98,102,103,101
%N A003188 Decimal equivalent of Gray code for n.
%C A003188 Inverse of sequence A006068 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 A003188 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003188 M. W. Bunder et al., On binary reflected Gray codes and functions, Discr. 
               Math., 308 (2008), 1690-1700.
%D A003188 M. Gardner, Mathematical Games, Sci. Amer. Vol. 227 (No. 2, Feb. 1972), 
               p. 107.
%D A003188 M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. 
               Freeman, NY, 1986, p. 15.
%D A003188 J. A. Oteo and J. Ros, A Fractal Set from the Binary Reflected Gray Code, 
               J. Phys. A: Math Gen. 38 (2005) 8935-8949.
%H A003188 N. J. A. Sloane, <a href="b003188.txt">Table of n, a(n) for n = 0..1000</
               a>
%H A003188 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A003188 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A003188 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%H A003188 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A003188 a(n) = 2*a([n/2])+A021913(n-1) - Henry Bottomley (se16(AT)btinternet.com), 
               Apr 05 2001
%F A003188 a(n) = n XOR floor(n/2), where XOR is the binary exclusive OR operator. 
               - Paul D. Hanna (pauldhanna(AT)juno.com), Jun 04 2002
%F A003188 G.f.: 1/(1-x) * sum(k>=0, 2^k*x^2^k/(1+x^2^(k+1))). - Ralf Stephan, May 
               06 2003
%F A003188 a(0)=0, a(2n) = 2a(n) + [n odd], a(2n+1) = 2a(n) + [n even]. - Ralf Stephan 
               (ralf(AT)ark.in-berlin.de), Oct 20 2003
%F A003188 a(n) = sum(k=1, n, 2^A007814(k) * (-1)^((k/2^A007814(k)-1)/2)). - Ralf 
               Stephan (ralf(AT)ark.in-berlin.de), Oct 29 2003
%F A003188 a(0) = 0, a(n+1) = a(n) XOR 2^A007814(n) - Jaume Simon Gispert (jaume(AT)nuem.com), 
               Sep 11 2004
%F A003188 Inverse of sequence A006068. - Philippe DELEHAM, Apr 29 2005
%p A003188 with(combinat); graycode(6); # to produce first 64 terms
%p A003188 printf(cat(` %.6d`$64), op(map(convert, graycode(6), binary))); lprint(); 
               # to produce binary strings
%o A003188 (PARI) a(n)=sum(k=1,n,(-1)^((k/2^valuation(k,2)-1)/2)*2^valuation(k,2))
%Y A003188 a(2*A003714(n)) = 3*A003714(n) for all n. - Antti Karttunen, Apr 26 1999
%Y A003188 Same sequence in binary: A014550, bisection: A048724. Cf. A038554, A048641, 
               A048642.
%Y A003188 Sequence in context: A083362 A153142 A154447 this_sequence A154435 A006042 
               A100280
%Y A003188 Adjacent sequences: A003185 A003186 A003187 this_sequence A003189 A003190 
               A003191
%K A003188 nonn,nice,easy
%O A003188 0,3
%A A003188 N. J. A. Sloane (njas(AT)research.att.com).
%E A003188 More terms from Larry Reeves (Larryr(AT)acm.org), Sep 05 2000

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