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Search: id:A119920
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| A119920 |
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Number of rationals in [0, 1) having exactly n preperiodic bits, then exactly n periodic bits. |
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+0
1
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| 1, 4, 24, 96, 480, 1728, 8064, 30720, 129024, 506880, 2095104, 8232960, 33546240, 133152768, 536248320, 2139095040, 8589803520, 34285289472, 137438429184, 549212651520, 2198882746368, 8791793860608, 35184363700224
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = 2^(n-1) * sum_{d|n} (2^d - 1) * mu(n/d)
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EXAMPLE
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The binary expansion of 7/24 = 0.010(01)... has 3 preperiodic bits (to the right of the binary point) followed by 2 periodic (i.e., repeating) bits, while 1/2 = 0.1(0)... has one bit of each type. The preperiodic and periodic parts are both chosen to be as short as possible.
a(2) = |{1/12 = 0.00(01)..., 5/12 = 0.01(10)..., 7/12 = 0.10(01)..., 11/12 = 0.11(10)...}| = 4
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MATHEMATICA
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Table[2^(n-1)(Plus@@((2^Divisors[n]-1)MoebiusMu[n/Divisors[n]])), {n, 1, 23} ]
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CROSSREFS
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Elementwise product of 2^n (offset 0) and A038199. Also, diagonal of A119918.
Sequence in context: A054603 A100381 A091143 this_sequence A100738 A139238 A139231
Adjacent sequences: A119917 A119918 A119919 this_sequence A119921 A119922 A119923
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KEYWORD
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nonn,base,easy
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AUTHOR
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Brad Chalfan (brad(AT)chalfan.net), May 28, 2006
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