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 A161893 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. 0
 4, 3, 18, 22, 30, 9, 11, 50, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS EXAMPLE First few terms of sequence are: 1/4,1/3,7/18,9/22,13/30,4/9,5/11,23/50,7/15,... CROSSREFS Cf. A161892, A161621 Sequence in context: A130515 A302851 A276083 * A192773 A183231 A241358 Adjacent sequences:  A161890 A161891 A161892 * A161894 A161895 A161896 KEYWORD nonn,frac AUTHOR Daniel Tisdale, Jun 21 2009 STATUS approved

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Last modified October 31 08:46 EDT 2020. Contains 338101 sequences. (Running on oeis4.)