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A242303
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Decimal expansion of C(4), where C(x) = -Sum{k>=1} (-1)^k/p_k^x and p_k is the k-th prime.
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6
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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
(list;
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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.
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LINKS
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Table of n, a(n) for n=-1..23.
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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0.05137830516674828257520007...
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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).
Sequence in context: A174879 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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STATUS
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approved
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