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Search: id:A030109
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| A030109 |
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Write n in binary, reverse bits, subtract 1, divide by 2. |
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+0
6
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| 0, 0, 1, 0, 2, 1, 3, 0, 4, 2, 6, 1, 5, 3, 7, 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15, 0, 16, 8, 24, 4, 20, 12, 28, 2, 18, 10, 26, 6, 22, 14, 30, 1, 17, 9, 25, 5, 21, 13, 29, 3, 19, 11, 27, 7, 23, 15, 31, 0, 32, 16, 48, 8, 40, 24, 56, 4, 36, 20, 52, 12, 44, 28, 60, 2, 34, 18, 50
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The sequence divides naturally into blocks of length 2^k, k = 0, 1, 2, ... On block k, let n go from 0 to 2^k-1, write n in binary using k bits and reverse the bits. - N. J. A. Sloane (njas(AT)research.att.com), Jun 11 2002.
For example: the 3-bit strings are 000, 001, 010, 011, 100, 101, 110 and 111. When they are bit-reversed, we get 000, 100, 010, 110, 001, 101, 011, 111. Or, in decimal representation 0,4,2,6,1,5,3,7.
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FORMULA
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a(n) = A059893(n)-A053644(n). If 2*2^k<= n<3*2^k then a(n) = 2*a(n-2^k); if 3*2^k<= n<4*2^k then a(n) = 1+ a(n-2^k) starting with a(1) = 0. - Henry Bottomley (se16(AT)btinternet.com), Sep 13 2001
a(2n) = a(n), a(2n+1) = a(n) + 2^[log2(n)]. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 22 2003
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EXAMPLE
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0; 0,1; 0,2,1,3; 0,4,2,6,1,5,3,7; 0,8,4,12,2,10,6,14,1,9,5,13,3,11,7,15; ...
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CROSSREFS
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Cf. A030101. A049773 is another version.
Sequence in context: A108202 A025480 A088002 this_sequence A058208 A070817 A127474
Adjacent sequences: A030106 A030107 A030108 this_sequence A030110 A030111 A030112
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KEYWORD
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nonn,base,tabf
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.
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