A244274 -id:A244274 - cp's OEIS frontend

A347952 Decimal expansion of exp(1) * (gamma - Ei(-1)).

2, 1, 6, 5, 3, 8, 2, 2, 1, 5, 3, 2, 6, 9, 3, 6, 3, 5, 9, 4, 2, 0, 9, 8, 6, 3, 4, 8, 4, 9, 2, 4, 3, 0, 5, 6, 8, 3, 8, 1, 4, 2, 0, 7, 6, 7, 7, 4, 1, 4, 4, 3, 6, 9, 0, 2, 3, 0, 1, 3, 9, 1, 7, 1, 8, 9, 4, 9, 4, 2, 4, 2, 5, 7, 9, 7, 7, 9, 8, 7, 1, 7, 9, 7, 6, 9, 2, 6, 0, 3, 5, 1, 4, 1, 5, 5, 6, 7, 5, 7, 2, 6, 7, 6, 4, 7, 5, 3, 4, 8

Offset: 1

Ilya Gutkovskiy, Oct 23 2021

			2.16538221532693635942098634849243056838142076774144369...

Cf. A001008, A001113, A001620, A002805, A073003, A099285, A239069, A244274, A348573.

RealDigits[Exp[1] (EulerGamma - ExpIntegralEi[-1]), 10, 110] [[1]]

exp(1)*(Euler + eint1(1)) \\ Michel Marcus, Oct 24 2021

Equals Sum_{k>=1} H(k) / k!, where H(k) is the k-th harmonic number.

Equals -Integral_{x=0..1} exp(x)*log(1-x) dx. - Amiram Eldar, Oct 23 2021

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

Original entry on oeis.org

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

Stanislav Sykora, Jun 29 2014

			4.709300169327103330744143217754700463516616783290647196...

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

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.

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

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

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

PARI
```
exp(1)/Euler
```

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

cp's OEIS Frontend

A347952 Decimal expansion of exp(1) * (gamma - Ei(-1)).

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