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A085548
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Decimal expansion of the prime zeta function at 2.
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21
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4, 5, 2, 2, 4, 7, 4, 2, 0, 0, 4, 1, 0, 6, 5, 4, 9, 8, 5, 0, 6, 5, 4, 3, 3, 6, 4, 8, 3, 2, 2, 4, 7, 9, 3, 4, 1, 7, 3, 2, 3, 1, 3, 4, 3, 2, 3, 9, 8, 9, 2, 4, 2, 1, 7, 3, 6, 4, 1, 8, 9, 3, 0, 3, 5, 1, 1, 6, 5, 0, 2, 7, 3, 6, 3, 9, 1, 0, 8, 7, 4, 4, 4, 8, 9, 5, 7, 5, 4, 4, 3, 5, 4, 9, 0, 6, 8, 5, 8, 2, 2, 2, 8, 0, 6
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 94-98
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LINKS
| H. Cohen, High Precision Computation of Hardy-Littlewood Constants, Preprint.
X. Gourdon and P. Sebah, Some Constants from Number theory
Gerhard Niklasch and Pieter Moree, Some number-theoretical constants [Cached copy]
Eric Weisstein's World of Mathematics, Prime Zeta Function
Eric Weisstein's World of Mathematics, Distinct Prime Factors
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FORMULA
| P(2) = Sum_{p prime>=2} 1/p^2 = Sum_{n=1..inf} mobius(n)*log(zeta(2*n))/n - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003
Equals A085991 + A086032 +1/4. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 22 2010]
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EXAMPLE
| 0.4522474200410654985065...
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MATHEMATICA
| (* If Mathematica version >= 7.0 then RealDigits[PrimeZetaP[2]//N[#, 105]&][[1]] else : *)
m = 200; $MaxExtraPrecision = 200; PrimeZetaP[s_] := NSum[MoebiusMu[k]*Log[Zeta[k*s]]/k, {k, 1, m},
AccuracyGoal -> m, NSumTerms -> m, PrecisionGoal -> m, WorkingPrecision -> m];
RealDigits[PrimeZetaP[2]][[1]][[1 ;; 105]]
(* From Jean-François Alcover, Jun 24 2011 *)
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PROG
| (PARI) recip2(n) = { v=0; p=1; forprime(y=2, n, v=v+1./y^2; ); print(v) }
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CROSSREFS
| Cf. A085541.
Sequence in context: A156890 A163531 A016715 * A074459 A155793 A070593
Adjacent sequences: A085545 A085546 A085547 * A085549 A085550 A085551
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KEYWORD
| easy,nonn,cons
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Jul 03 2003
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003
Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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