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A079059 Decimal expansion of product( p == 3 (mod 4), sqrt(1-p^-2)). +0
1
9, 2, 5, 2, 6, 1 (list; cons; graph; listen)
OFFSET

0,1

COMMENT

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]

REFERENCES

E. Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition: Chelsea, New York (1974), pp. 641-669

LINKS

E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.

FORMULA

product( p == 3 (mod 4), sqrt(1-p^-2))=0.92526...

PROGRAM

(PARI) prod(k=1, 40000, if(prime(k)%4-3, 1, sqrt(1-prime(k)^-2)))

CROSSREFS

Cf. A071903.

Sequence in context: A111188 A089065 A154398 this_sequence A154838 A082831 A085551

Adjacent sequences: A079056 A079057 A079058 this_sequence A079060 A079061 A079062

KEYWORD

cons,more,nonn

AUTHOR

Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003

EXTENSIONS

Corrected offset and leading zero R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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