

A242303


Decimal expansion of C(4), where C(x) = Sum{k>=1} (1)^k/p_k^x and p_k is the kth 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 primesrelated 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



