login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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,...

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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