OFFSET
2,3
COMMENTS
The sum converges rapidly to 1/2. For 100 summands, S(n) = 0.4992...; for 500, S(n) = 0.49995...
EXAMPLE
First few fractions 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}]
PROG
(PARI) a(n) = numerator(sum(k=2, n, (primepi((k+1)^2) - primepi(k^2))/(primepi((k+1)^2)*primepi(k^2)))); \\ Michel Marcus, Aug 15 2022
CROSSREFS
KEYWORD
nonn,frac,less
AUTHOR
Daniel Tisdale, Jun 21 2009
EXTENSIONS
Offset 2 and more terms from Michel Marcus, Aug 15 2022
STATUS
approved