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A242301 Decimal expansion of C(2), where C(x) = -Sum{k>=1} (-1)^k/p_k^x and p_k is the k-th prime. 10
1, 6, 2, 8, 1, 6, 2, 4, 6, 6, 6, 3, 6, 0, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

The next digits of C(2), after ...6014, seem to converge to a(16)=1, a(17)=5.

LINKS

Table of n, a(n) for n=0..15.

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

Eric Weisstein's World of Mathematics, Prime Sums

Eric Weisstein's World of Mathematics, Prime Zeta Function

Wikipedia, Prime Zeta Function

EXAMPLE

0.1628162466636014...

PROG

(PARI) See Sykora link.

CROSSREFS

Cf. A078437 (x=1), A242302 (x=3), A242303 (x=4), A242304 (x=5).

Sequence in context: A270138 A177889 A086744 * A256129 A019692 A031259

Adjacent sequences:  A242298 A242299 A242300 * A242302 A242303 A242304

KEYWORD

nonn,cons,hard,more

AUTHOR

Stanislav Sykora, May 14 2014

STATUS

approved

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Last modified March 30 18:30 EDT 2017. Contains 284302 sequences.