A268683 Decimal expansion of (sqrt(2) - 1)/2.

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

Offset

0,1

Comments

This is the maximum increase in mass-energy a particle can carry away from a neutral rotating (Kerr) black hole via the Penrose process.

Apart from leading digits the same as A174968, A157214 and A010503. - R. J. Mathar, Feb 24 2016

References

Subrahmanyan Chandrasekhar, The Mathematical Theory of Black Holes, Oxford, 1983, pp. 368-369.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Stijn J. van Tongeren, Rotating black holes (2009).

Wikipedia, Penrose process.

Index entries for algebraic numbers, degree 2.

Formula

From Amiram Eldar, May 14 2026: (Start)

Equals A188582/2 = 1/A090488.

Minimal polynomial: 4*x^2 + 4*x - 1. (End)

Example

0.20710678118654752440084436210484903928483593768847403658833986899536623...

Mathematica

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

Prog

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

Crossrefs

Cf. A090488, A174968, A188582, A268682.

Sequence in context: A192496 A390653 A156442 * A174968 A254445 A346670

Adjacent sequences: A268680 A268681 A268682 * A268684 A268685 A268686

Keyword

nonn,cons,easy

Author

Charles R Greathouse IV, Feb 19 2016

Extensions

More digits from Jon E. Schoenfield, Mar 15 2018

Status

approved