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Search: id:A161893
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| A161893 |
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Denominators of the partial sums of S(n) = Sum[(Pi((n+1)^2) - Pi(n^2))/(Pi((n+1)^2)*Pi(n^2)), n from 2 to oo. Pi(n) = number of primes <= n. |
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1
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OFFSET
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1,1
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COMMENT
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The sum converges rapidly to 1/2. For 100 summands, S(n)= 0.4992...; for 500, S(n) = 0.49995...S(n) generalizes to: S_k(n)= Sum[(Pi((n+k)^2)-Pi((n+k-1)^2))/(Pi((n+k)^2)*Pi((n+k-1)^2)))-?-> 1/Pi((k+1)^2),n=2 to oo, k =1,2,3,... For k =1, the analogous series for C(n),composites <= n, appears to converge to 1.
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EXAMPLE
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First few terms of sequence are: 1/4,1/3,7/18,9/22,13/30,4/9,5/11,23/50,7/15,...
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CROSSREFS
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Cf. A161892, A161621
Sequence in context: A113203 A034486 A130515 this_sequence A167479 A076589 A052039
Adjacent sequences: A161890 A161891 A161892 this_sequence A161894 A161895 A161896
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KEYWORD
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nonn,frac
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AUTHOR
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Daniel Tisdale (daniel6874(AT)gmail.com), Jun 21 2009
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