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

Author

Paolo Xausa, Nov 05 2024

Keywords

• nonn
• cons
• easy

Examples

			0.1565176427496656518180806234654239164560069706202...
		

Links

• 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.

Crossrefs

Cf. A000796, A001113, A072334.

Cf. A027641, A027642, A073747.

Programs

Mathematica

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

PARI

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

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)