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A246686 Decimal expansion of 'mu', a percolation constant associated with the asymptotic threshold for 3-dimensional bootstrap percolation. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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.

Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]

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: A153615 A281531 A248914 * A048649 A200008 A086751

Adjacent sequences:  A246683 A246684 A246685 * A246687 A246688 A246689

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Sep 01 2014

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)