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 A242302 Decimal expansion of C(3), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x. 6
 9, 3, 4, 6, 3, 6, 3, 1, 3, 9, 9, 6, 4, 9, 8, 8, 9, 1, 1, 2, 4, 9, 0, 3, 3, 1, 3, 9, 2, 4, 6, 5, 5, 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(3), after ...91124, seem to converge to a(20)=9, a(21)=0. After ...9033139246557, the next digit, a(33), seems likely to be 7 or 8. - Jon E. Schoenfield, Dec 28 2017 LINKS S. Sykora, PARI/GP scripts for primes-related functions, see function AltSum1DivPrimePwr(x,eps), with instruction EXAMPLE 0.09346363139964988911249033139246557... MATHEMATICA next = 0; ndigits = 11; epsilon = 10^-(2 ndigits); k = 1; While[test = 1/Prime[k + 1]^3 - 1/Prime[k]^3; -test > epsilon,   next = next + test; k += 2]; First[RealDigits[-next, 10, ndigits]] (* Robert Price, Sep 07 2019 *) PROG (PARI) See Sykora link. CROSSREFS Cf. A078437 (x=1), A242301 (x=2), A242303 (x=4), A242304 (x=5). Sequence in context: A273017 A222233 A021111 * A102754 A225455 A154184 Adjacent sequences:  A242299 A242300 A242301 * A242303 A242304 A242305 KEYWORD nonn,cons,hard,more AUTHOR Stanislav Sykora, May 14 2014 EXTENSIONS a(20)-a(32) from Jon E. Schoenfield, Dec 28 2017 STATUS approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)