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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 (list; constant; graph; refs; listen; history; text; internal format)
 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 * A154838 A082831 A085551 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

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Last modified September 19 23:59 EDT 2019. Contains 327207 sequences. (Running on oeis4.)