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A242304 Decimal expansion of C(5), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x. 6


%S 2,7,3,9,9,2,2,2,6,1,4,5,4,2,7,4,0,5,8,6,2,7,3,6,0,9,6,8,4,6,6,9,7,4,

%T 0,2,5,5,9,2,1,2,2,7,7,0,1,1,2,9,9,9,8,5,4,1,5

%N Decimal expansion of C(5), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x.

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

%C The next digits of C(5), after ...46697, seem to converge to a(32)=4, a(33)=0.

%C a(56), the next digit after ...85415, appears to be a 4. - _Jon E. Schoenfield_, Dec 30 2017

%H S. Sykora, <a href="https://oeis.org/wiki/File:PrimesRelatedFunctions.txt">PARI/GP scripts for primes-related functions</a>, see function AltSum1DivPrimePwr(x,eps), with instructions

%e = 0.0273992226145427405862736096846697402559212277...

%t Sum[ N[ -(-1)^k/(Prime[k]^5), 64], {k, 1000000000}] (* _Robert G. Wilson v_, Nov 06 2016 *)

%o (PARI) See Sykora link.

%o (PARI) sumalt(k=1, (-1)^k/prime(k)^5) \\ _Michel Marcus_, Nov 06 2016

%Y Cf. A078437 (x=1), A242301 (x=2), A242302 (x=3), A242303 (x=4).

%K nonn,cons,hard,more

%O -1,1

%A _Stanislav Sykora_, May 14 2014

%E a(32)-a(43) from _Robert G. Wilson v_, Nov 06 2016

%E a(44)-a(55) from _Jon E. Schoenfield_, Dec 30 2017

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)