

A242302


Decimal expansion of C(3), where C(x) = Sum{k>=1} (1)^k/p_k^x and p_k is the kth prime.


6



9, 3, 4, 6, 3, 6, 3, 1, 3, 9, 9, 6, 4, 9, 8, 8, 9, 1, 1, 2, 4
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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(3), after ...91124, seem to converge to a(20)=9, a(21)= 0.


LINKS

Table of n, a(n) for n=1..19.
S. Sykora, PARI/GP scripts for primesrelated functions, see function AltSum1DivPrimePwr(x,eps), with instruction


EXAMPLE

0.0934636313996498891124...


PROG

(PARI) See Sykora link.


CROSSREFS

Cf. A078437 (x=1), A242301 (x=2), A242303 (x=4), A242304 (x=5).
Sequence in context: A273017 A222233 A021111 * A102754 A225455 A154184
Adjacent sequences: A242299 A242300 A242301 * A242303 A242304 A242305


KEYWORD

nonn,cons,hard,more


AUTHOR

Stanislav Sykora, May 14 2014


STATUS

approved



