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 A340711 Decimal expansion of Product_{primes p == 3 (mod 5)} (p^2+1)/(p^2-1). 11
 1, 2, 7, 3, 9, 8, 6, 6, 1, 3, 2, 0, 6, 8, 3, 3, 9, 2, 5, 1, 5, 8, 1, 6, 8, 3, 8, 2, 1, 3, 8, 9, 4, 7, 2, 7, 3, 4, 7, 6, 2, 7, 4, 4, 4, 6, 7, 6, 7, 3, 5, 7, 8, 9, 4, 0, 0, 2, 9, 6, 8, 1, 4, 4, 0, 9, 8, 7, 4, 8, 6, 6, 8, 1, 5, 3, 7, 7, 6, 0, 6, 9, 5, 5, 6, 2, 0, 1, 2, 2, 8, 5, 4, 3, 8, 1, 1, 4, 6, 6, 0, 7, 3, 0, 5, 9, 2, 7, 4, 0, 5, 9, 2, 2, 4, 4, 6, 8, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..500 Salma Ettahri, Olivier Ramaré, and Léon Surel, Fast multi-precision computation of some Euler product, arXiv:1908.06808 [math.NT], 2019, p. 20. Steven Finch, Quartic and Octic Characters Modulo n, arXiv:1008.2547 [math.NT], 2007-2010 p. 11 (formula on kappa(5) and kappa(-5)). Steven Finch, Greg Martin and Pascal Sebah, Roots of unity and nullity modulo n, Proc. Amer. Math. Soc. Volume 138, Number 8, August 2010, pp. 2729-2743. Steven Finch and Pascal Sebah, Residue of a Mod 5 Euler Product, arXiv:0912.3677 [math.NT], 2009 (formulas). Alessandro Languasco and Alessandro Zaccagnini, A note on Mertens' formula for arithmetic progressions, Journal of Number Theory Volume 127, Issue 1, (2007), 37-46. Alessandro Languasco and Alessandro Zaccagnini, On the constant in the Mertens product for arithmetic progressions. II: Numerical values, Math. Comp. 78 (2009), 315-326. Alessandro Languasco and Alessandro Zaccagnini, On the constant in the Mertens product for arithmetic progressions. I. Identities, Funct. Approx. Comment. Math. Volume 42, Number 1 (2010), 17-27. Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens constants - more than 100 correct digits, (2007), 1-134 (digital data). Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens constants mod q; 3 <= q <= 100, (2007) (GP-PARI procedure 100 digits accuracy). Richard J. Mathar,  Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015. Doug S. Phillips and Peter Zvengrowski, Convergence of Dirichlet Series and Euler Products, Contributions Section of Natural Mathematical and Biotechnical Sciences 38(2):153 (2017). FORMULA D = Product_{primes p == 0 (mod 5)} (p^2+1)/(p^2-1) = 13/12. E = Product_{primes p == 1 (mod 5)} (p^2+1)/(p^2-1) = A340629. F = Product_{primes p == 2 (mod 5)} (p^2+1)/(p^2-1) = A340710. G = Product_{primes p == 3 (mod 5)} (p^2+1)/(p^2-1) = this constant. H = Product_{primes p == 4 (mod 5)} (p^2+1)/(p^2-1) = A340628. D*E*F*G*H = 5/2. E*F*G*H = 30/13. D*E*H = sqrt(5)/2. D*F*G = 13*sqrt(5)/12. F*G = sqrt(5). E*H = 6*sqrt(5)/13. Equals Sum_{q in A004617} 2^A001221(q)/q^2. - R. J. Mathar, Jan 27 2021 EXAMPLE 1.273986613206833925158... MATHEMATICA (* Using Vaclav Kotesovec's function Z from A301430. *) \$MaxExtraPrecision = 1000; digits = 121; digitize[c_] := RealDigits[Chop[N[c, digits]], 10, digits - 1][]; digitize[1/(Z[5, 3, 4]/Z[5, 3, 2]^2)] CROSSREFS Cf. A175646, A175647, A248930, A248938, A301429, A333240, A334826, A335963, A340576, A340577, A340578, A340628, A340629, A340004, A340127, A340710. Sequence in context: A021891 A256614 A021369 * A242304 A227415 A309156 Adjacent sequences:  A340708 A340709 A340710 * A340712 A340713 A340714 KEYWORD nonn,cons AUTHOR Artur Jasinski, Jan 16 2021 STATUS approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)