|
%I #53 Oct 30 2022 23:04:36
%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
%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.
%H Stanislav 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).
%Y Cf. A085965.
%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
|
