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A242303 Decimal expansion of C(4), where C(x) = -Sum{k>=1} (-1)^k/p_k^x and p_k is the k-th prime. 6
5, 1, 3, 7, 8, 3, 0, 5, 1, 6, 6, 7, 4, 8, 2, 8, 2, 5, 7, 5, 2, 0, 0, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-1,1

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(4), after ...20007, seem to converge to a(24)=0, a(25)= 5.

LINKS

Table of n, a(n) for n=-1..23.

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

EXAMPLE

0.05137830516674828257520007...

PROG

(PARI) See Sykora link.

CROSSREFS

Cf. A078437 (x=1), A242301 (x=2), A242302 (x=3), A242304 (x=5).

Sequence in context: A174879 A094136 A051996 * A214803 A225984 A074048

Adjacent sequences:  A242300 A242301 A242302 * A242304 A242305 A242306

KEYWORD

nonn,cons,hard,more

AUTHOR

Stanislav Sykora, May 14 2014

STATUS

approved

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Last modified August 20 03:34 EDT 2017. Contains 290823 sequences.