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A242303
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Decimal expansion of C(4), where C(x) = -Sum_{k>=1} (-1)^k/prime(k)^x.
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7
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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
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OFFSET
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-1,1
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=-1..43.
S. Sykora, PARI/GP scripts for primes-related functions, see function AltSum1DivPrimePwr(x,eps), with instructions
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EXAMPLE
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0.0513783051667482825752000705647313696928183994...
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MATHEMATICA
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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 *)
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PROG
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(PARI) See Sykora link.
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CROSSREFS
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Cf. A078437 (x=1), A242301 (x=2), A242302 (x=3), A242304 (x=5).
Cf. A085964.
Sequence in context: A327965 A094136 A051996 * A214803 A225984 A074048
Adjacent sequences: A242300 A242301 A242302 * A242304 A242305 A242306
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KEYWORD
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nonn,cons,hard,more
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AUTHOR
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Stanislav Sykora, May 14 2014
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EXTENSIONS
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a(24)-a(43) from Jon E. Schoenfield, Dec 30 2017
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STATUS
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approved
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