A268682 - OEIS

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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

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OFFSET

0,1

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

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

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

EXAMPLE