A244499 Decimal expansion of e/gamma, the ratio of Euler number and the Euler-Mascheroni constant.

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

Author

Stanislav Sykora, Jun 29 2014

Keywords

• nonn
• cons
• easy

Examples

			4.709300169327103330744143217754700463516616783290647196...
		

References

• Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 1.10, page 2.

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..2019
• 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.

Crossrefs

Cf. A001008, A001113, A001620, A002805, A073004, A080130, A244274.

Programs

Magma

R:= RealField(100); Exp(1)/EulerGamma(R); // G. C. Greubel, Aug 30 2018

Mathematica

RealDigits[E/EulerGamma, 10, 100][[1]] (* G. C. Greubel, Aug 30 2018 *)

PARI

exp(1)/Euler

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