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%I #22 Sep 08 2022 08:45:51
%S 2,5,1,8,8,1,6,7,6,9,0,9,0,3,8,0,0,7,4,4,9,5,9,3,4,5,3,5,4,1,7,7,8,0,
%T 3,7,8,8,4,3,3,3,6,0,2,1,3,6,1,3,3,2,6,4,8,8,0,4,5,9,8,9,1,5,5,4,9,7,
%U 2,1,4,4,3,1,4,8,9,6,6,6,5,2,3,0,3,8,3,2,0,9,5,2,4,4,4,7,5,6,5,6,8,7,9,9,2,0
%N Decimal expansion of sqrt(2)*e^(gamma), where gamma is Euler's constant.
%C This constant appears when comparing various divergent series after n iterations.
%H G. C. Greubel, <a href="/A174815/b174815.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MersennePrime.html">Mersenne Prime</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant">Euler-Mascheroni constant</a>
%F lim_{n->oo} e^sum(1/k, k=1..n) / sqrt(1+2+3+...+n) = sqrt(2)*e^gamma.
%e sqrt(2)*e^(gamma) = 2.5188167690903800744959345354177803788433360213612...
%p evalf(sqrt(2)*exp(gamma),99);
%t RealDigits[Sqrt[2]*Exp[EulerGamma], 10, 100][[1]] (* _G. C. Greubel_, Sep 06 2018 *)
%o (PARI) sqrt(2)*exp(Euler) \\ _Charles R Greathouse IV_, Aug 01 2011
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2)* Exp(EulerGamma(R)); // _G. C. Greubel_, Sep 06 2018
%Y Equals A002193*A001113^A001620.
%K nonn,cons
%O 1,1
%A Ryan Gerard (rsgerard(AT)gmail.com), Mar 29 2010
%E Comments containing infinities removed by _Jonathan Sondow_, Aug 01 2011
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