A185393 Decimal expansion of e/(e-1) = 1 + 1/e + 1/e^2 + ...

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

Offset: 1

Author

Charles R Greathouse IV, Mar 20 2012

Keywords

• nonn
• cons
• easy

Examples

			1.58197670686932642438500200510901155854686930107539613626678705964804...
		

References

• Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.29.a) pp. 286 and 307.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Wikipedia, Tannery's theorem.
• Index entries for transcendental numbers

Crossrefs

Cf. A254445, A254446, A320349, A320350.

Apart from 1st digit the same as A073333.

Programs

Mathematica

RealDigits[E/(E - 1), 10, 100][[1]] (* G. C. Greubel, Jun 29 2017 *)

PARI

exp(1)/(exp(1)-1)

Python

from sympy import E
print(list(map(int, str((E/(E-1)).n(88))[:-1].replace(".", "")))) # Michael S. Branicky, May 25 2022

Formula

Equals Sum_{n>=0} 1/exp(n). - Vaclav Kotesovec, Jan 30 2015

From Vaclav Kotesovec, Oct 13 2018: (Start)

Equals 1 - LambertW(exp(1/(1 - exp(1))) / (1 - exp(1))).

Equals -LambertW(-1, exp(1/(1 - exp(1))) / (1 - exp(1))).

(End)

Equals Sum_{k>=0} (-1)^k*B(k)/k!, where B(k) is the k-th Bernoulli number. - Amiram Eldar, May 08 2021

Equals Integral_{x=0..oo} exp(-floor(x)) dx (Monier). - Bernard Schott, May 08 2022

Equals lim_{n->oo} Sum_{k=1..n} (k/n)^n (via Tannery's theorem). - Stoyan Apostolov, May 24 2022