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Search: id:A030101
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| A030101 |
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a(n) is the number produced when n is converted to base 2, reversed and then converted back to base 10. |
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+0
55
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| 0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 13, 3, 11, 7, 15, 1, 17, 9, 25, 5, 21, 13, 29, 3, 19, 11, 27, 7, 23, 15, 31, 1, 33, 17, 49, 9, 41, 25, 57, 5, 37, 21, 53, 13, 45, 29, 61, 3, 35, 19, 51, 11, 43, 27, 59, 7, 39, 23, 55, 15, 47, 31, 63, 1, 65, 33, 97, 17, 81, 49, 113, 9, 73, 41, 105, 25, 89, 57
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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As with decimal reversal initial zeros are ignored, otherwise the reverse of 1 would be 1000000... ad infinitum.
Numerators of the binary van der Corput sequence. - Eric S Rowland (erowland(AT)math.rutgers.edu), Feb 12 2008
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REFERENCES
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Solutions to 17th USA Mat. Olympiad, Math. Mag., 62 (1989), 210-214 (#3).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
Michael Gilleland, Some Self-Similar Integer Sequences
Wikipedia, van der Corput sequence.
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FORMULA
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a(n) = 0, a(2n) = a(n), a(2n+1) = a(n) + 2^([log2(n)]+1). For n>0, a(n) = 2*A030109(n) - 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 15 2003
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EXAMPLE
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a(100) = 19 because 100 (base 10) = 1100100 (base 2) and R(1100100 (base 2)) = 10011 (base 2) = 19 (base 10)
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MATHEMATICA
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Table[FromDigits[Reverse[IntegerDigits[i, 2]], 2], {i, 0, 80}]
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PROGRAM
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(PARI) a(n)=if(n<1, 0, subst(Polrev(binary(n)), x, 2))
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CROSSREFS
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Cf. A030109, A036044, A056539, A004086.
Sequence in context: A040026 A106609 A093474 this_sequence A162742 A081432 A136655
Adjacent sequences: A030098 A030099 A030100 this_sequence A030102 A030103 A030104
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KEYWORD
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nonn,base,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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