A073747 -id:A073747 - cp's OEIS frontend

A361873 Decimal representation of continued fraction 1, 4, 7, 10, 13, 16, 19, ... (A016777).

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

Offset: 1

Kelvin Voskuijl, Mar 27 2023

			1.24149571957930311301996637630645032348085867125361348645459...

Cf. A016777.

Cf. A060997, A073747.

RealDigits[1 + BesselI[4/3, 2/3]/BesselI[1/3, 2/3], 10, 120][[1]]

Equals 1 + BesselI(4/3, 2/3)/BesselI(1/3, 2/3).

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

Original entry on oeis.org

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

Paolo Xausa, Nov 05 2024

			0.1565176427496656518180806234654239164560069706202...

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.

Cf. A000796, A001113, A072334.

Cf. A027641, A027642, A073747.

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

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

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)

A378909 Decimal expansion of 1/sqrt(tanh(1)).

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Dec 10 2024

			1.145877517669027008315306752403764242145795236598...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 3.6.5, p. 223.

Index entries for transcendental numbers

Cf. A073744, A073747.

Mathematica
```
RealDigits[1/Sqrt[Tanh[1]],10,100][[1]]
```

Equals sqrt(A073747). - Hugo Pfoertner, Dec 10 2024

cp's OEIS Frontend

A361873 Decimal representation of continued fraction 1, 4, 7, 10, 13, 16, 19, ... (A016777).

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

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A378909 Decimal expansion of 1/sqrt(tanh(1)).

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