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A242624 Decimal expansion of Product_{n>1} (1-1/n)^(1/n).

%I A242624 #33 Nov 30 2024 16:45:33
%S A242624 4,5,4,5,1,2,1,8,0,5,1,4,6,4,6,3,1,7,0,3,2,8,0,1,4,6,3,6,8,4,3,2,7,3,
%T A242624 9,9,3,0,7,5,8,6,8,1,2,2,6,9,9,5,4,4,3,6,0,4,9,3,4,8,9,2,3,6,5,9,2,7,
%U A242624 0,7,6,1,5,1,1,2,3,2,6,2,5,1,5,6,1,0,0,1,5,4,0,9,6,0,5,5,4,2,4,9
%N A242624 Decimal expansion of Product_{n>1} (1-1/n)^(1/n).
%D A242624 Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9, pp. 121-122.
%H A242624 G. C. Greubel, <a href="/A242624/b242624.txt">Table of n, a(n) for n = 0..1000</a>
%F A242624 From _Amiram Eldar_, Feb 06 2022: (Start)
%F A242624 Equals exp(-A085361).
%F A242624 Equals 1/A245254. (End)
%e A242624 0.4545121805146463170328014636843273993...
%p A242624 evalf(exp(-sum((1-Zeta(n))/(1-n), n=2..infinity)), 120); # _Vaclav Kotesovec_, Dec 11 2015
%t A242624 Exp[-NSum[(1-Zeta[n])/(1-n), {n, 2, Infinity}, NSumTerms -> 300, WorkingPrecision -> 110]] // RealDigits[#, 10, 100]& // First
%o A242624 (PARI) default(realprecision, 100); exp(suminf(n=2, (zeta(n)-1)/(1-n))) \\ _G. C. Greubel_, Nov 15 2018
%o A242624 (Magma) SetDefaultRealField(RealField(100)); L:=RiemannZeta();  Exp((&+[(Evaluate(L,n)-1)/(1-n): n in [2..10^3]])); // _G. C. Greubel_, Nov 15 2018
%o A242624 (Sage) numerical_approx(exp(sum((zeta(k)-1)/(1-k) for k in [2..1000])), digits=100) # _G. C. Greubel_, Nov 15 2018
%Y A242624 Cf. A085361, A242623, A244625, A245254.
%K A242624 nonn,cons
%O A242624 0,1
%A A242624 _Jean-François Alcover_, May 19 2014
%E A242624 Mma modified and data extended by _Jean-François Alcover_, May 23 2014