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A278389 Decimal expansion of 1/(1*2) - 1/(2*3) + 1/(3*5) - 1/(4*7) + 1/(5*11) - ... -(-1)^k/(k*prime(k)) - ... 0
3, 7, 4, 4, 8, 5, 1, 8, 7, 9, 7, 4, 7, 4, 6, 1, 6, 3, 2, 1, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Alternating sum of the reciprocals of the products of k and the k-th prime.

The next five digits after ...63217 seem likely to be 0, 9, 4, 0, 6.

LINKS

Table of n, a(n) for n=0..20.

Eric Weisstein's World of Mathematics, Prime Sums

FORMULA

-Sum_{k>=1} (-1)^k/(k*prime(k)).

EXAMPLE

0.374485187974746163217...

MATHEMATICA

RealDigits[N[-Sum[(-1)^k/(k*Prime[k]), {k, 1, 8*10^6}], 30]][[1]] (* G. C. Greubel, Nov 22 2016 *)

CROSSREFS

See the following for alternating sums of reciprocals of primes, composites, and related expressions: A078437 (primes), A242301 (primes^2), A242302 (primes^3), A242303 (primes^4), A242304 (primes^5), A269229 (composites), A275110 (composites excluding prime powers), A275712 (nonprimes), A276494 (composites^2).

Sequence in context: A256676 A267412 A087941 * A021271 A238274 A094689

Adjacent sequences:  A278386 A278387 A278388 * A278390 A278391 A278392

KEYWORD

nonn,cons,hard,more

AUTHOR

Jon E. Schoenfield, Nov 20 2016

STATUS

approved

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Last modified February 22 06:17 EST 2018. Contains 299430 sequences. (Running on oeis4.)