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A185380
Decimal expansion of sum 1/(p*(p+2)) over the primes p.
3
2, 6, 3, 6, 7, 2, 0, 6, 1, 7, 6, 1, 1, 5, 3, 1, 7, 8, 7, 4, 9, 8, 4, 2, 1, 8, 8, 2, 3, 3, 7, 7, 6, 7, 5, 3, 0, 8, 7, 4, 9, 6, 3, 1, 8, 3, 9, 6, 7, 5, 6, 8, 0, 2, 1, 2, 2, 2, 3, 8, 1, 2, 6, 8, 3, 2, 2, 4, 3, 8, 9, 8, 1, 6, 3, 2, 2, 9, 8, 2, 4, 9, 8, 3, 9, 2, 2, 6, 6, 1, 7, 5, 4, 5, 1, 8, 0, 9, 6, 4, 0, 0, 6, 9, 9, 4
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
read("transforms") ;
Digits := 300 ;
# insert coding of ZetaM(s, M) and Hurw(a) from A179119 here...
A185380 := proc()
Hurw(2) ;
end proc:
PROG
(PARI) sumeulerrat(1/(p*(p+2))) \\ Amiram Eldar, Mar 19 2021
CROSSREFS
Cf. A136141 (1/(p(p-1))), A179119 (1/(p(p+1))).
Sequence in context: A274439 A280342 A275476 * A373058 A136695 A337115
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Jan 21 2013
EXTENSIONS
More digits from Vaclav Kotesovec, Jan 13 2021
STATUS
approved