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A340794 Decimal expansion of Product_{primes p == 2 (mod 5)} p^2/(p^2-1).

%I A340794 #24 Jan 27 2021 01:45:10
%S A340794 1,3,6,8,5,7,2,0,5,3,8,7,6,6,4,9,0,8,5,8,6,0,7,6,3,8,9,0,4,8,3,1,0,9,
%T A340794 9,9,0,1,7,0,2,0,7,8,2,8,8,8,5,8,9,5,2,0,5,0,0,8,5,0,4,0,2,9,5,5,6,3,
%U A340794 3,1,1,8,8,8,1,0,5,4,2,1,2,0,9,2,1,5,6,7,7,4,9,6,0,8,0,9,7,3,8,1,1,9,4,4,2,9,3,2,4,3,5,1,5,4,0,9,3,2,2,6
%N A340794 Decimal expansion of Product_{primes p == 2 (mod 5)} p^2/(p^2-1).
%H A340794 Vaclav Kotesovec, <a href="/A340794/b340794.txt">Table of n, a(n) for n = 1..501</a>
%H A340794 For links see A340711.
%F A340794 I = Product_{primes p == 0 (mod 5)} p^2/(p^2-1) = 25/24.
%F A340794 J = Product_{primes p == 1 (mod 5)} p^2/(p^2-1) = A340004.
%F A340794 K = Product_{primes p == 2 (mod 5)} p^2/(p^2-1) = this constant.
%F A340794 L = Product_{primes p == 3 (mod 5)} p^2/(p^2-1) = A340665.
%F A340794 M = Product_{primes p == 4 (mod 5)} p^2/(p^2-1) = A340127.
%F A340794 I*J*K*L*M = Pi^2/6 = zeta(2).
%F A340794 J*K*L*M = 4*Pi^2/25.
%F A340794 M = (Pi/2)*C(5,4)^(-2)*exp(-gamma/2)*sqrt(3/log(2+sqrt(5))), where gamma is the Euler-Mascheroni constant A001620 and C(5,4) is the Mertens constant = 1.29936454791497798816084...
%F A340794 Equals Sum_{k>=1} 1/A004616(k)^2. - _Amiram Eldar_, Jan 24 2021
%e A340794 1.36857205387664908586076389048310999017020782888589520500850402955633118881...
%t A340794 (* Using Vaclav Kotesovec's function Z from A301430. *)
%t A340794 $MaxExtraPrecision = 1000; digits = 121;
%t A340794 digitize[c_] := RealDigits[Chop[N[c, digits]], 10, digits - 1][[1]];
%t A340794 digitize[Z[5, 2, 2]]
%Y A340794 Cf. A004616, A175646, A175647, A248930, A248938, A301429, A333240, A334826, A335963, A340127, A340576, A340577, A340578, A340628, A340629, A340665, A340710, A340711.
%K A340794 nonn,cons
%O A340794 1,2
%A A340794 _Artur Jasinski_, Jan 21 2021