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 A246686 #16 May 27 2025 03:31:56
%S A246686 4,0,3,9,1,2,7,2,0,2,9,8,7,5,5,8,3,7,9,3,2,1,1,4,2,0,7,4,4,9,5,3,4,9,
%T A246686 8,8,7,1,0,2,7,1,9,2,9,3,7,7,5,4,3,2,6,4,4,1,1,4,4,6,8,8,4,6,3,3,6,8,
%U A246686 6,3,0,7,0,1,2,9,4,0,2,3,6,5,9,3,7,6,9,6,2,1,6,8,0,6,4,3,0,5,0,5,4
%N A246686 Decimal expansion of 'mu', a percolation constant associated with the asymptotic threshold for 3-dimensional bootstrap percolation.
%D A246686 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.18 Percolation Cluster Density Constants, pp. 371-378.
%H A246686 J. Balogh, B. Bollobás and R. Morris, <a href="https://arxiv.org/abs/0806.4485">Bootstrap percolation in three dimensions.</a> arXiv:0806.4485 [math.CO], 2008-2009.
%H A246686 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2024; p. 47.
%H A246686 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BootstrapPercolation.html">Bootstrap Percolation</a>
%F A246686 Equals -Integral_{0..oo} log(1/2 - exp(-2*x)/2 + (1/2)*sqrt(1 + exp(-4*x) - 4*exp(-3*x) + 2*exp(-2*x))) dx.
%e A246686 0.4039127202987558379321142074495349887102719293775432644...
%t A246686 mu = -NIntegrate[Log[1/2 - Exp[-2*x]/2 + (1/2)*Sqrt[1 + Exp[-4*x] - 4*Exp[-3*x] + 2 *Exp[-2*x]]] , {x, 0, Infinity}, WorkingPrecision -> 101]; RealDigits[mu] // First
%Y A246686 Cf. A086463 (analog 2-dimensional percolation constant).
%K A246686 nonn,cons,easy
%O A246686 0,1
%A A246686 _Jean-François Alcover_, Sep 01 2014