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%I #16 Mar 26 2022 10:17:18
%S 4,7,0,9,3,0,0,1,6,9,3,2,7,1,0,3,3,3,0,7,4,4,1,4,3,2,1,7,7,5,4,7,0,0,
%T 4,6,3,5,1,6,6,1,6,7,8,3,2,9,0,6,4,7,1,9,6,0,9,7,8,7,0,3,8,7,1,4,8,8,
%U 1,8,3,6,1,2,4,9,5,8,1,1,6,3,1,3,8,8,5,4,8,8,1,9,2,3,6,0,7,2,0,3,0,1,7,5,7
%N Decimal expansion of e/gamma, the ratio of Euler number and the Euler-Mascheroni constant.
%D Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 1.10, page 2.
%H Stanislav Sykora, <a href="/A244499/b244499.txt">Table of n, a(n) for n = 1..2019</a>
%H Ovidiu Furdui, <a href="https://www.jstor.org/stable/27643000">Problem 1764</a>, Mathematics Magazine, Vol. 80, No. 1 (2007), pp. 77-78; <a href="https://www.jstor.org/stable/27643084">Euler-Mascheroni meets e</a>, Solution to Problem 1764 by Edward Schmeichel, ibid., Vol. 81, No. 1 (2008), p. 67.
%F Equals lim_{n->oo} (g(n)^gamma/gamma^g(n))^(2*n), where g(n) = H(n) - log(n) and H(n) = A001008(n)/A002805(n) is the n-th harmonic number (Furdui, 2007 and 2013). - _Amiram Eldar_, Mar 26 2022
%e 4.709300169327103330744143217754700463516616783290647196...
%t RealDigits[E/EulerGamma, 10, 100][[1]] (* _G. C. Greubel_, Aug 30 2018 *)
%o (PARI) exp(1)/Euler
%o (Magma) R:= RealField(100); Exp(1)/EulerGamma(R); // _G. C. Greubel_, Aug 30 2018
%Y Cf. A001008, A001113, A001620, A002805, A073004, A080130, A244274.
%K nonn,cons,easy
%O 1,1
%A _Stanislav Sykora_, Jun 29 2014
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