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

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

0,1

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

Links

Table of n, a(n) for n=0..86.

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

E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1 and vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.

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]

Prog

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

Crossrefs

Cf. A071903.

Sequence in context: A154398 A225412 A176019 * A342574 A154838 A082831

Adjacent sequences: A079056 A079057 A079058 * A079060 A079061 A079062

Keyword

cons,nonn

Author

Benoit Cloitre, Feb 02 2003

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

Status

approved