OFFSET
0,1
COMMENTS
If we omit the first term 1/(2*4)=0.125 from the sum, 0.138672... remains, which is an upper limit of A209329 in the sense that we "fake" prime gaps of 2 here [which are actually larger on average].
FORMULA
Equals -1/8 + Sum_{k>=2} (-1)^k * 2^(k-2) * P(k), where P is the prime zeta function. - Vaclav Kotesovec, Jan 13 2021
EXAMPLE
0.263672061761153178749842188233776 .. = 1/(2*4) +1/(3*5) + 1/(5*7) + 1/(7*9) + 1/(11*13)+ ...
MAPLE
PROG
(PARI) sumeulerrat(1/(p*(p+2))) \\ Amiram Eldar, Mar 19 2021
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Jan 21 2013
EXTENSIONS
More digits from Vaclav Kotesovec, Jan 13 2021
STATUS
approved