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%I #32 Apr 23 2023 20:15:12
%S 4,3,8,5,4,0,5,1,6,4,3,3,1,1,4,8,3,0,1,7,5,8,5,6,7,8,5,2,0,9,1,1,9,2,
%T 1,3,2,3,4,2,8,9,6,1,3,0,7,4,8,4,6,8,3,1,8,4,5,8,4,0,9,2,3,9,5,4,9,1,
%U 2,0,3,2,9,2,5,7,1,4,3,6,2,8,6,7,1,2,8,8,4,1,0,6,5,7,8,5,6,4,1,2,3,2,6,8,0
%N Decimal expansion of (e^gamma - 1)/e^gamma.
%C The value is equal to lim_{n->oo} (Sum_{d|n#, d>n} 1/phi(d))/(Sum_{d|n#} 1/phi(d)).
%H G. C. Greubel, <a href="/A227242/b227242.txt">Table of n, a(n) for n = 0..5000</a>
%F From _Alois P. Heinz_, Feb 24 2022: (Start)
%F Equals 1 - exp(-gamma) = 1 - A080130.
%F Equals lim_{n->oo} A351901(n)/A000142(n). (End)
%e (exp(gamma) - 1)/exp(gamma) = 0.438540516433114830175856785....
%p evalf(1-exp(-gamma), 120); # _Alois P. Heinz_, Feb 24 2022
%t RealDigits[(E^EulerGamma - 1)/E^EulerGamma, 10, 50][[1]] (* _G. C. Greubel_, Oct 02 2017 *)
%o (Magma) E:=EulerGamma(RealField(105)); Reverse(Intseq(Floor(10^105*(Exp(E)-1)/Exp(E))))
%o (PARI) default(realprecision, 105); x=10*(exp(Euler)-1)/exp(Euler); for(n=1, 105, d=floor(x); x=(x-d)*10; print1(d, ", "));
%Y Cf. A000142, A001113, A001620, A073004, A080130, A351901.
%K nonn,cons
%O 0,1
%A _Arkadiusz Wesolowski_, Oct 19 2013
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