cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A079059 Decimal expansion of product( p == 3 (mod 4), sqrt(1-p^-2)).

Original entry on oeis.org

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, 5, 9, 7, 5, 3, 2, 7, 7, 0, 3, 5, 1, 4, 1, 6, 8, 0, 4, 9, 5
Offset: 0

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Author

Benoit Cloitre, Feb 02 2003

Keywords

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, 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

Crossrefs

Cf. A071903.

Programs

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

Formula

product( p == 3 (mod 4), sqrt(1-p^-2)) = 0.92526...
Equals 1/(sqrt(2)*A064533) = A010503/A064533. [R. J. Mathar, Jul 29 2010]

Extensions

Corrected offset and leading zero R. J. Mathar, Jan 31 2009
More digits from R. J. Mathar, Jul 28 2010
More digits, using the Jul 29 2010 formula from R. J. Mathar, from Jon E. Schoenfield, Nov 05 2016
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