

A161892


Numerators 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.


1




OFFSET

1,3


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+k1)^2))/(Pi((n+k)^2)*Pi((n+k1)^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

Table of n, a(n) for n=1..9.


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,...


MATHEMATICA

Table[Sum[(PrimePi[(i+1)^2]PrimePi[i^2])/(PrimePi[(i+1)^2]*PrimePi[i^2]), {i, 2, j}], {j, 2, 50}]


CROSSREFS

Cf. A161621
Sequence in context: A121056 A174189 A112529 * A056528 A055565 A196088
Adjacent sequences: A161889 A161890 A161891 * A161893 A161894 A161895


KEYWORD

nonn,frac


AUTHOR

Daniel Tisdale, Jun 21 2009


STATUS

approved



