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%I #7 Dec 10 2023 17:28:50
%S 7,3,5,8,4,0,3,0,6,8,0,6,4,9,8,9,3,4,0,3,7,6,1,7,8,1,6,5,4,0,2,4,1,0,
%T 4,3,7,1,2,9,6,3,1,9,1,0,0,3,4,9,3,4,4,1,8,1,7,8,6,8,6,2,7,7,0,8,8,6,
%U 6,0,5,8,3,7,9,8,4,1,3,7,2,0,4,8,1,0,5
%N Decimal expansion of (1 + Product_{p prime} (1 - 2/(p*(p+1))))/2.
%C The asymptotic density of numbers k such that A046660(k) is even (A162644).
%C Detrey et al. (2016) calculated 1000 decimal digits of this constant.
%H Jérémie Detrey, Pierre-Jean Spaenlehauer and Paul Zimmermann, <a href="https://members.loria.fr/PZimmermann/papers/rho.pdf">Computing the rho constant</a>, 2016.
%H Michael J. Mossinghoff and Timothy S. Trudgian, <a href="https://arxiv.org/abs/1906.02847">A tale of two omegas</a>, arXiv:1906.02847 [math.NT], 2019. See page 9.
%F Equals (1 + A065472/zeta(2))/2.
%F Equals lim_{n->oo} A340818(n)/A340819(n).
%e 0.735840306806498934037617816540241043712963191003493...
%o (PARI) (prodeulerrat(1 - 2/(p*(p+1))) + 1)/2
%Y Cf. A013661, A046660, A065472, A162644, A340818, A340819.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Jan 22 2021
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