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Decimal expansion of e^(2*EulerGamma).
4

%I #22 Feb 27 2024 03:57:28

%S 3,1,7,2,2,1,8,9,5,8,1,2,5,4,5,0,5,2,7,7,2,7,9,1,3,4,0,9,0,6,9,4,7,4,

%T 9,7,7,1,2,2,9,5,7,7,3,7,7,7,2,3,0,0,4,5,8,5,1,4,7,7,8,2,8,8,4,1,9,2,

%U 5,2,1,4,4,1,1,6,3,8,9,4,6,3,6,6,4,6,3,8,1,7,8,7,5,0,8,4,8,9,6,6,6,5

%N Decimal expansion of e^(2*EulerGamma).

%H Robert Price, <a href="/A091724/b091724.txt">Table of n, a(n) for n = 1..10000</a>

%H Jean-Marie De Koninck and Florian Luca, <a href="https://eudml.org/doc/284003">On the composition of the Euler function and the sum of divisors function</a>, Colloquium Mathematicum, Vol. 108, No. 1 (2007), pp. 31-51.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.

%F Equals lim_{x -> 0} e^(2*ExpIntegralEi(-x))/x^2.

%F Equals A073004^2. - _Michel Marcus_, Jun 25 2021

%F Equals lim sup_{n->oo} H(n)/log_2(n)^2, where H(n) = A370689(n)/A370690(n) (De Koninck and Luca, 2007). - _Amiram Eldar_, Feb 27 2024

%e 3.17221895812545052772791340906947497712295773777230...

%t RealDigits[Exp[2*EulerGamma], 10, 100][[1]] (* _Amiram Eldar_, Jun 25 2021 *)

%o (PARI) exp(2*Euler) \\ _Michel Marcus_, Jun 25 2021

%Y Cf. A001620, A073004, A370689, A370690.

%K nonn,cons

%O 1,1

%A _Eric W. Weisstein_, Feb 01 2004