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A346745 Decimal expansion of Product_{k>=2} (1 - 1/k^12).

%I A346745 #18 Aug 06 2024 05:56:52
%S A346745 9,9,9,7,5,3,9,1,3,9,2,1,8,9,3,2,5,6,0,0,3,4,4,8,5,7,0,6,4,1,9,0,9,7,
%T A346745 2,7,1,8,0,3,3,9,7,1,1,4,7,2,6,0,9,9,5,3,7,2,5,5,6,3,1,3,8,7,4,0,7,6,
%U A346745 0,1,0,3,6,5,7,8,4,2,5,7,0,7,2,8,6,9,5
%N A346745 Decimal expansion of Product_{k>=2} (1 - 1/k^12).
%H A346745 Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a> (2011).
%F A346745 Equals sinh(Pi) * cosh(Pi*sqrt(3)/2)^2 * (cosh(Pi) - cos(Pi*sqrt(3))) / (24*Pi^5).
%F A346745 Equals exp(Sum_{j>=1} (1 - zeta(12*j))/j). - _Vaclav Kotesovec_, Aug 01 2021
%e A346745 0.999753913921893256003448570641909727180...
%p A346745 evalf(sinh(Pi) * cosh(Pi*sqrt(3)/2)^2 * (cosh(Pi) - cos(Pi*sqrt(3))) / (24*Pi^5), 120); # _Vaclav Kotesovec_, Aug 01 2021
%t A346745 RealDigits[Sinh[Pi]*Cosh[Pi*Sqrt[3]/2]^2*(Cosh[Pi] - Cos[Pi*Sqrt[3]])/(24*Pi^5), 10, 120][[1]] (* _Amiram Eldar_, Jun 12 2023 *)
%o A346745 (PARI) exp(suminf(j=1, (1 - zeta(12*j))/j)) \\ _Vaclav Kotesovec_, Aug 01 2021
%Y A346745 Cf. A109219, A175615, A175616, A175617, A175618, A175619, A339745.
%K A346745 nonn,cons
%O A346745 0,1
%A A346745 _Sean A. Irvine_, Jul 31 2021