|
| |
|
|
A003188
|
|
Decimal equivalent of Gray code for n.
(Formerly M2250)
|
|
45
| |
|
|
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, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| 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
|
|
|
REFERENCES
| M. W. Bunder et al., On binary reflected Gray codes and functions, Discr. Math., 308 (2008), 1690-1700.
M. Gardner, Mathematical Games, Sci. Amer. Vol. 227 (No. 2, Feb. 1972), p. 107.
M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 15.
J. A. Oteo and J. Ros, A Fractal Set from the Binary Reflected Gray Code, J. Phys. A: Math Gen. 38 (2005) 8935-8949.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..1000
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences that are permutations of the natural numbers
Paul Tarau, Isomorphic Data Encodings and their Generalization to Hylomorphisms on Hereditarily Finite Data Types
|
|
|
FORMULA
| a(n) = 2*a([n/2])+A021913(n-1) - Henry Bottomley, Apr 05 2001
a(n) = n XOR floor(n/2), where XOR is the binary exclusive OR operator. - Paul D. Hanna, Jun 04 2002
G.f.: 1/(1-x) * sum(k>=0, 2^k*x^2^k/(1+x^2^(k+1))). - Ralf Stephan, May 06 2003
a(0)=0, a(2n) = 2a(n) + [n odd], a(2n+1) = 2a(n) + [n even]. - Ralf Stephan, Oct 20 2003
a(0)=0, a(n) = 2 a(floor(n/2)) + mod(floor((n+1)/2), 2).
a(n) = sum(k=1, n, 2^A007814(k) * (-1)^((k/2^A007814(k)-1)/2)). - Ralf Stephan, Oct 29 2003
a(0) = 0, a(n+1) = a(n) XOR 2^A007814(n) - Jaume Simon Gispert (jaume(AT)nuem.com), Sep 11 2004
Inverse of sequence A006068. - Philippe DELEHAM, Apr 29 2005
a(n) = a(n-1) XOR A006519(n). - Franklin T. Adams-Watters, Jul 18 2011.
|
|
|
MAPLE
| with(combinat); graycode(6); # to produce first 64 terms
printf(cat(` %.6d`$64), op(map(convert, graycode(6), binary))); lprint(); # to produce binary strings
|
|
|
MATHEMATICA
| f[n_] := BitXor[n, Floor[n/2]]; Array[f, 70, 0] (* From Robert G. Wilson v, Jun 09 2010 *)
|
|
|
PROG
| (PARI) a(n)=bitxor(n, n>>1);
(PARI) a(n)=sum(k=1, n, (-1)^((k/2^valuation(k, 2)-1)/2)*2^valuation(k, 2))
(C) int a(int n) { return n ^ (n>>1); }
|
|
|
CROSSREFS
| a(2*A003714(n)) = 3*A003714(n) for all n. - Antti Karttunen, Apr 26 1999
Same sequence in binary: A014550, bisection: A048724. Cf. A038554, A048641, A048642.
Sequence in context: A204939 A153142 A154447 * A154435 A006042 A100280
Adjacent sequences: A003185 A003186 A003187 * A003189 A003190 A003191
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Larry Reeves (Larryr(AT)acm.org), Sep 05 2000
|
| |
|
|
