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Search: id:A006068
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| A006068 |
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a(n) is Gray-coded into n.
(Formerly M2253)
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+0
12
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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; listen)
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OFFSET
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0,3
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COMMENT
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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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1023
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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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
A066194(n) = a(n-1) + 1, n>=1 . - Philippe DELEHAM, Apr 29 2005
Inverse of sequence A003188 . - Philippe DELEHAM, Apr 29 2005
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EXAMPLE
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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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CROSSREFS
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Cf. A038554, A005811, A003188, A014550, A003100.
Adjacent sequences: A006065 A006066 A006067 this_sequence A006069 A006070 A006071
Sequence in context: A099896 A160679 A153141 this_sequence A154436 A072764 A130328
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), Jan 10 2001
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