Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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