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Search: id:A079059
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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
1
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OFFSET
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0,1
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COMMENT
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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
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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
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E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
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FORMULA
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product( p == 3 (mod 4), sqrt(1-p^-2))=0.92526...
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PROGRAM
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(PARI) prod(k=1, 40000, if(prime(k)%4-3, 1, sqrt(1-prime(k)^-2)))
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CROSSREFS
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Cf. A071903.
Sequence in context: A111188 A089065 A154398 this_sequence A154838 A082831 A085551
Adjacent sequences: A079056 A079057 A079058 this_sequence A079060 A079061 A079062
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KEYWORD
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cons,more,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003
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EXTENSIONS
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Corrected offset and leading zero R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009
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