This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268682 #65 Jan 24 2025 09:42:15
%S A268682 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,
%T A268682 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,
%U A268682 3,7,6,0,7,6,8,9,4,6,4,8,0,5,7,4,8,0,6
%N A268682 Decimal expansion of 1 - 1/sqrt(2).
%C A268682 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.
%C A268682 Differs from A157215 only in one or two leading digits. - _R. J. Mathar_, Feb 24 2016
%C A268682 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
%D A268682 Charles D. Dermer and Govind Menon, High Energy Radiation from Black Holes: Gamma Rays, Cosmic Rays, and Neutrinos (2009). See pp. 400-402.
%H A268682 G. C. Greubel, <a href="/A268682/b268682.txt">Table of n, a(n) for n = 0..10000</a>
%H A268682 Anthony Van Duzer, <a href="https://arxiv.org/abs/1904.05525">Subtrees of a Given size in Schroeder Trees</a>, arXiv:1904.05525 [math.CO], 2019.
%H A268682 Stijn J. van Tongeren, <a href="http://www.staff.science.uu.nl/~proko101/StijnJvanTongeren_bh3.pdf">Rotating black holes</a> (2009).
%H A268682 Wikipedia, <a href="https://en.wikipedia.org/wiki/Penrose_process">Penrose process</a>
%H A268682 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A268682 Equals 1 - A010503.
%F A268682 a(n) = 9 - A010503(n). - _Philippe Deléham_, Feb 21 2016
%F A268682 Equals Integral_{x=0..Pi/4} sin(x) dx. - _Amiram Eldar_, Jun 29 2020
%e A268682 0.29289321881345247559915563789515096071516406231152596341166013100463376...
%t A268682 RealDigits[1 - 1 / Sqrt[2], 10, 90] [[1]] (* _Vincenzo Librandi_, Feb 20 2016 *)
%o A268682 (PARI) 1-sqrt(.5)
%o A268682 (Magma) 1-1/Sqrt(2); // _Vincenzo Librandi_, Feb 20 2016
%Y A268682 Cf. A010503, A268683.
%K A268682 nonn,cons,easy
%O A268682 0,1
%A A268682 _Charles R Greathouse IV_, Feb 19 2016
%E A268682 More digits from _Jon E. Schoenfield_, Mar 15 2018