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
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.
Crossrefs
Cf. A071903.
Programs
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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...
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
Comments