A246686 Decimal expansion of 'mu', a percolation constant associated with the asymptotic threshold for 3-dimensional bootstrap percolation.

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, 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, 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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.18 Percolation Cluster Density Constants, pp. 371-378.

Links

Table of n, a(n) for n=0..100.

J. Balogh, B. Bollobás and R. Morris, Bootstrap percolation in three dimensions. arXiv:0806.4485v2 [math.CO] 31 Aug 2009

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 47.

Eric Weisstein's MathWorld, Bootstrap Percolation

Formula

-integral_{0..infinity} log(1/2 - exp(-2*x)/2 + (1/2)*sqrt(1 + exp(-4*x) - 4*exp(-3*x) + 2*exp(-2*x))) dx.

Example

0.4039127202987558379321142074495349887102719293775432644...

Mathematica

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

Crossrefs

Cf. A086463 (analog 2-dimensional percolation constant).

Sequence in context: A376643 A248914 A373462 * A048649 A200008 A086751

Adjacent sequences: A246683 A246684 A246685 * A246687 A246688 A246689

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2014

Status

approved