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A079059
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Decimal expansion of product( p == 3 (mod 4), sqrt(1-p^-2)).
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0
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9, 2, 5, 2, 6, 1, 5, 7, 4, 7, 5, 7, 0, 4, 8, 6, 2, 2, 6, 2, 7, 0, 7, 0, 4, 2, 2, 9, 6, 6, 9, 6, 3, 4, 4, 2, 6, 4, 2, 4, 7, 3, 4, 7, 8, 7, 8, 8, 6, 5, 1, 1, 1, 4, 0, 6, 6, 3, 3, 0, 8, 8, 5, 9, 9, 1, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The complementary product_{p== 1 (mod 4)} sqrt(1-1/p^2) = 0.97303... is related: 0.925261....*0.97303... = sqrt(4/3)/sqrt(Zeta(2)) = 10*A020832/sqrt(A013661). [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009]
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REFERENCES
| E. Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition: Chelsea, New York (1974), pp. 641-669
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LINKS
| E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
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FORMULA
| product( p == 3 (mod 4), sqrt(1-p^-2))=0.92526...
Equals 1/(sqrt(2)*A064533) = A010503/A064533. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 29 2010]
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PROG
| (PARI) prod(k=1, 40000, if(prime(k)%4-3, 1, sqrt(1-prime(k)^-2)))
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CROSSREFS
| Cf. A071903.
Sequence in context: A089065 A154398 A176019 * A154838 A082831 A085551
Adjacent sequences: A079056 A079057 A079058 * A079060 A079061 A079062
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KEYWORD
| cons,more,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003
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EXTENSIONS
| Corrected offset and leading zero R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009
More digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 28 2010
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