

A242301


Decimal expansion of C(2), where C(x) = Sum{k>=1} (1)^k/prime(k)^x.


11



1, 6, 2, 8, 1, 6, 2, 4, 6, 6, 6, 3, 6, 0, 1, 4, 1, 5, 7, 6, 8, 3, 3, 5
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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.
The next digit after ...15768335 seems most likely to be an 8.  Jon E. Schoenfield, Dec 27 2017


LINKS

Table of n, a(n) for n=0..23.
S. Sykora, PARI/GP scripts for primesrelated 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

0.162816246663601415768335...


MATHEMATICA

k = 1; p = 2; s = 0; While[p < 1000000000, s = N[s + (1)^k/p^2, 40]; k = Mod[++k, 2]; p = NextPrime@ p]; s (* takes ~30 minutes on an average laptop to 18 decimal digits *)(* Robert G. Wilson v, Dec 30 2017 *)


PROG

(PARI) See Sykora link.


CROSSREFS

Cf. A078437 (x=1), A242302 (x=3), A242303 (x=4), A242304 (x=5).
Cf. A085548.
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


EXTENSIONS

a(16)a(23) from Jon E. Schoenfield, Dec 27 2017


STATUS

approved



