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

1,1

References

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

Links

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.

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

Crossrefs

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

Sequence in context: A153117 A338926 A322166 * A303173 A285778 A147864

Adjacent sequences: A244496 A244497 A244498 * A244500 A244501 A244502

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Jun 29 2014

Status

approved