A377635 Decimal expansion of 1/(exp(2) - 1).

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

Offset

0,2

Links

Table of n, a(n) for n=0..89.

Michael Penn, One of my favorite identities, YouTube video, 2023.

Michael Ian Shamos, Shamos's catalog of the real numbers, 2011, p. 218.

Index entries for transcendental numbers

Index entries for sequences related to zeta function.

Formula

Equals 1/(A072334 - 1).

Equals Sum_{k >= 1} (-1)^(k+1)*zeta(2*k)/Pi^(2*k).

From Amiram Eldar, Nov 08 2024: (Start)

Formulas from Shamos (2011):

Equals (coth(1) - 1)/2 = (A073747 - 1)/2.

Equals Sum_{k>=1} exp(-2*k).

Equals Sum_{k>=1} 1/(k^2*Pi^2 + 1).

Equals Sum_{k>=0} B(k)*2^(k-1)/k!, where B(k) = A027641(k)/A027642(k) is the k-th Bernoulli number. (End)

Example

0.1565176427496656518180806234654239164560069706202...

Mathematica

First[RealDigits[1/(Exp[2] - 1), 10, 100]]

Prog

(PARI) 1/(exp(2) - 1) \\ Amiram Eldar, Nov 08 2024

Crossrefs

Cf. A000796, A001113, A072334.

Cf. A027641, A027642, A073747.

Sequence in context: A293009 A011004 A226975 * A273065 A071629 A087496

Adjacent sequences: A377632 A377633 A377634 * A377636 A377637 A377638

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 05 2024

Status

approved