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 A242304 Decimal expansion of C(5), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x. 7
 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, 0, 2, 5, 5, 9, 2, 1, 2, 2, 7, 7, 0, 1, 1, 2, 9, 9, 9, 8, 5, 4, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET -1,1 COMMENTS The alternating series of reciprocal powers of prime numbers converge for any x > 0 (absolutely so if x > 1) but are hard to compute. The next digits of C(5), after ...46697, seem to converge to a(32)=4, a(33)=0. a(56), the next digit after ...85415, appears to be a 4. - Jon E. Schoenfield, Dec 30 2017 LINKS S. Sykora, PARI/GP scripts for primes-related functions, see function AltSum1DivPrimePwr(x,eps), with instructions EXAMPLE = 0.0273992226145427405862736096846697402559212277... MATHEMATICA Sum[ N[ -(-1)^k/(Prime[k]^5), 64], {k, 1000000000}] (* Robert G. Wilson v, Nov 06 2016 *) PROG (PARI) See Sykora link. (PARI) sumalt(k=1, (-1)^k/prime(k)^5) \\ Michel Marcus, Nov 06 2016 CROSSREFS Cf. A078437 (x=1), A242301 (x=2), A242302 (x=3), A242303 (x=4). Cf. A085965. Sequence in context: A256614 A021369 A340711 * A227415 A309156 A298042 Adjacent sequences:  A242301 A242302 A242303 * A242305 A242306 A242307 KEYWORD nonn,cons,hard,more AUTHOR Stanislav Sykora, May 14 2014 EXTENSIONS a(32)-a(43) from Robert G. Wilson v, Nov 06 2016 a(44)-a(55) from Jon E. Schoenfield, Dec 30 2017 STATUS approved

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Last modified June 18 13:35 EDT 2021. Contains 345112 sequences. (Running on oeis4.)