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A079059
Decimal expansion of product( p == 3 (mod 4), sqrt(1-p^-2)).
0
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
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
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