login
A244499
Decimal expansion of e/gamma, the ratio of Euler number and the Euler-Mascheroni constant.
2
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, 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, 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
OFFSET
1,1
REFERENCES
Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 1.10, page 2.
LINKS
Ovidiu Furdui, Problem 1764, Mathematics Magazine, Vol. 80, No. 1 (2007), pp. 77-78; Euler-Mascheroni meets e, Solution to Problem 1764 by Edward Schmeichel, ibid., Vol. 81, No. 1 (2008), p. 67.
FORMULA
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
EXAMPLE
4.709300169327103330744143217754700463516616783290647196...
MATHEMATICA
RealDigits[E/EulerGamma, 10, 100][[1]] (* G. C. Greubel, Aug 30 2018 *)
PROG
(PARI) exp(1)/Euler
(Magma) R:= RealField(100); Exp(1)/EulerGamma(R); // G. C. Greubel, Aug 30 2018
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, Jun 29 2014
STATUS
approved