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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 (list; constant; graph; refs; listen; history; text; internal format)
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].

LINKS

Table of n, a(n) for n=0..105.

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:

A185380() ;

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 * A136695 A337115 A154129

Adjacent sequences:  A185377 A185378 A185379 * A185381 A185382 A185383

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Jan 21 2013

EXTENSIONS

More digits from Vaclav Kotesovec, Jan 13 2021

STATUS

approved

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Last modified July 31 18:15 EDT 2021. Contains 346376 sequences. (Running on oeis4.)