A242304 - OEIS

A242304

Decimal expansion of C(5), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x.

2, 7, 3, 9, 9, 2, 2, 2, 6, 1, 4, 5, 4, 2, 7, 4, 0, 5, 8, 6, 2, 7, 3, 6, 0, 9, 6, 8, 4, 6, 6, 9, 7, 4, 0, 2, 5, 5, 9, 2, 1, 2, 2, 7, 7

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OFFSET

-1,1

COMMENTS

The alternating series of reciprocal powers of prime numbers converge for any x > 0 (absolutely so if x > 1) but are hard to compute.

The next digits of C(5), after ...46697, seem to converge to a(32)=4, a(33)=0.

LINKS

Stanislav Sykora, PARI/GP scripts for primes-related functions, see function AltSum1DivPrimePwr(x,eps), with instructions.

EXAMPLE

0.0273992226145427405862736096846697402559212277...

MATHEMATICA

Sum[ N[ -(-1)^k/(Prime[k]^5), 64], {k, 1000000000}] (* Robert G. Wilson v, Nov 06 2016 *)

PROG

(PARI) See Sykora link.

(PARI) sumalt(k=1, (-1)^k/prime(k)^5) \\ Michel Marcus, Nov 06 2016

CROSSREFS

Cf. A078437 (x=1), A242301 (x=2), A242302 (x=3), A242303 (x=4).

KEYWORD

nonn,cons,hard,more

AUTHOR

EXTENSIONS

a(32)-a(43) from Robert G. Wilson v, Nov 06 2016

STATUS

approved