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Search: id:A119918
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| A119918 |
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Table read by antidiagonals: number of rationals in [0, 1) having exactly n preperiodic bits, then exactly k periodic bits (read up antidiagonals). |
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+0
3
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| 1, 1, 2, 2, 2, 6, 4, 4, 6, 12, 8, 8, 12, 12, 30, 16, 16, 24, 24, 30, 54, 32, 32, 48, 48, 60, 54, 126, 64, 64, 96, 96, 120, 108, 126, 240, 128, 128, 192, 192, 240, 216, 252, 240, 504, 256, 256, 384, 384, 480, 432, 504, 480, 504, 990, 512, 512, 768, 768, 960, 864, 1008
(list; table; graph; listen)
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OFFSET
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1,3
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FORMULA
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a(n, k) = 2^max{0, n-1} * sum_{d|k} (2^d - 1) * mu(k/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, 2) = |{1/12 = 0.00(01)..., 5/12 = 0.01(10)..., 7/12 = 0.10(01)..., 11/12 = 0.11(10)...}| = 4
Table begins:
1 2 6 12
1 2 6 12
2 4 12 24
4 8 24 48
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MATHEMATICA
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Table[2^ Max[0, n-1](Plus@@((2^Divisors[k]-1)MoebiusMu[k/Divisors[k]])), {n, 0, 1 0}, {k, 1, 10}]
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CROSSREFS
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Outer product of A011782 and A038199.
Sequence in context: A158524 A054274 A053695 this_sequence A084867 A099259 A131904
Adjacent sequences: A119915 A119916 A119917 this_sequence A119919 A119920 A119921
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KEYWORD
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nonn,base,easy,tabl
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AUTHOR
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Brad Chalfan (brad(AT)chalfan.net), May 28, 2006
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