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A006068
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a(n) is Gray-coded into n.
(Formerly M2253)
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15
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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, 19, 18, 23, 22, 20, 21, 63, 62, 60, 61, 56, 57, 59, 58, 48, 49, 51, 50, 55, 54, 52, 53, 32, 33, 35, 34, 39, 38, 36, 37, 47, 46, 44, 45, 40, 41, 43, 42, 127, 126, 124, 125, 120, 121
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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'.
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
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1023
Paul Tarau, Isomorphic Data Encodings and their Generalization to Hylomorphisms on Hereditarily Finite Data Types
Index entries for sequences that are permutations of the natural numbers
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FORMULA
| 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.
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
a(n) XOR [a(n)/2] = n. [From Paul D. Hanna, Jan 18 2012]
A066194(n) = a(n-1) + 1, n>=1 . - Philippe DELEHAM, Apr 29 2005
Inverse of sequence A003188 . - Philippe DELEHAM, Apr 29 2005
a(n) = if n<2 then n else 2*m + (n mod 2 + m mod 2) mod 2, with m=a(floor(n/2)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 10 2010]
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EXAMPLE
| 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,...
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PROG
| (PARI) {a(n)=local(B=n); for(k=1, floor(log(n+1)/log(2)), B=bitxor(B, n\2^k)); B} /* Paul D. Hanna, Jan 18 2012 */
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CROSSREFS
| Cf. A038554, A005811, A003188, A014550, A003100.
Cf. A054429, A180200. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 15 2010]
Sequence in context: A099896 A160679 A153141 * A154436 A201566 A072764
Adjacent sequences: A006065 A006066 A006067 * A006069 A006070 A006071
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), Jan 10 2001
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