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

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

Table of n, a(n) for n=-1..43.

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).

Cf. A085965.

Sequence in context: A256614 A021369 A340711 * A227415 A361207 A309156

Adjacent sequences: A242301 A242302 A242303 * A242305 A242306 A242307

Keyword

nonn,cons,hard,more

Author

Stanislav Sykora, May 14 2014

Extensions

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

Status

approved