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 A242303 Decimal expansion of C(4), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x. 6
 5, 1, 3, 7, 8, 3, 0, 5, 1, 6, 6, 7, 4, 8, 2, 8, 2, 5, 7, 5, 2, 0, 0, 0, 7, 0, 5, 6, 4, 7, 3, 1, 3, 6, 9, 6, 9, 2, 8, 1, 8, 3, 9, 9, 4 (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(4), after ...20007, seem to converge to a(24)=0, a(25)= 5. a(44), the next digit after ...83994, appears to be a 2. - Jon E. Schoenfield, Dec 30 2017 LINKS S. Sykora, PARI/GP scripts for primes-related functions, see function AltSum1DivPrimePwr(x,eps), with instructions EXAMPLE 0.0513783051667482825752000705647313696928183994... MATHEMATICA next = 0; ndigits = 13; epsilon = 10^-(2 ndigits); k = 1; While[test = 1/Prime[k + 1]^4 - 1/Prime[k]^4; -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), A242302 (x=3), A242304 (x=5). Sequence in context: A327965 A094136 A051996 * A214803 A225984 A074048 Adjacent sequences:  A242300 A242301 A242302 * A242304 A242305 A242306 KEYWORD nonn,cons,hard,more AUTHOR Stanislav Sykora, May 14 2014 EXTENSIONS a(24)-a(43) from Jon E. Schoenfield, Dec 30 2017 STATUS approved

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Last modified October 14 02:19 EDT 2019. Contains 327994 sequences. (Running on oeis4.)