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Search: id:A119917
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| A119917 |
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Number of rationals in [0, 1) consisting just of repeating bits of period at most n. |
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+0
3
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| 1, 3, 9, 21, 51, 105, 231, 471, 975, 1965, 4011, 8031, 16221, 32475, 65205, 130485, 261555, 523131, 1047417, 2094957, 4191975, 8384229, 16772835, 33545715, 67100115, 134200785, 268418001, 536837061, 1073707971, 2147415981
(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) = sum_{i=1..n} sum_{d|i} (2^d - 1) * mu(i/d)
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EXAMPLE
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1/6 = 0.0010101... has repeating bits of period 2, but isn't counted because it has a preperiodic part (i.e., the repetition doesn't start immediately after the binary point). Also, 0 = 0.000... is counted and considered to have period 1.
a(1) = |{0 = 0.(0)...}| = 1
a(2) = |{0 = 0.(0)..., 1/3 = 0.(01)..., 2/3 = 0.(10)...}| = 3
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MATHEMATICA
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Table[Sum[Plus@@((2^Divisors[i]-1)MoebiusMu[i/Divisors[i]]), {i, 1, n}], {n, 1, 30 }]
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CROSSREFS
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Partial sums of A038199.
Adjacent sequences: A119914 A119915 A119916 this_sequence A119918 A119919 A119920
Sequence in context: A006813 A056823 A105544 this_sequence A111209 A109755 A005254
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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 29, 2006
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