A268682 Decimal expansion of 1 - 1/sqrt(2).

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

Offset: 0

Author

Charles R Greathouse IV, Feb 19 2016

Keywords

• nonn
• cons
• easy

Comments

This is the maximum fraction of mass-energy of a black hole which can come from angular momentum, and hence the maximum energy which can be extracted from the black hole via the Penrose process.

Differs from A157215 only in one or two leading digits. - R. J. Mathar, Feb 24 2016

This is the probability that a randomly selected vertex in a random Schroeder tree is a leaf as the number of leaves goes to infinity. See Corollary 2.1.2. of Van Duzer. - Michel Marcus, Apr 12 2019

Examples

			0.29289321881345247559915563789515096071516406231152596341166013100463376...
		

References

• Charles D. Dermer and Govind Menon, High Energy Radiation from Black Holes: Gamma Rays, Cosmic Rays, and Neutrinos (2009). See pp. 400-402.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Anthony Van Duzer, Subtrees of a Given size in Schroeder Trees, arXiv:1904.05525 [math.CO], 2019.
• Stijn J. van Tongeren, Rotating black holes (2009).
• Wikipedia, Penrose process
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A010503, A268683.

Programs

Magma

1-1/Sqrt(2); // Vincenzo Librandi, Feb 20 2016

Mathematica

RealDigits[1 - 1 / Sqrt[2], 10, 90] [[1]] (* Vincenzo Librandi, Feb 20 2016 *)

PARI

1-sqrt(.5)

Formula

Equals 1 - A010503.

a(n) = 9 - A010503(n). - Philippe Deléham, Feb 21 2016

Equals Integral_{x=0..Pi/4} sin(x) dx. - Amiram Eldar, Jun 29 2020

Extensions

More digits from Jon E. Schoenfield, Mar 15 2018