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A246686
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Decimal expansion of 'mu', a percolation constant associated with the asymptotic threshold for 3-dimensional bootstrap percolation.
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0
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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
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.18 Percolation Cluster Density Constants, pp. 371-378.
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LINKS
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FORMULA
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-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.
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EXAMPLE
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0.4039127202987558379321142074495349887102719293775432644...
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MATHEMATICA
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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
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CROSSREFS
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Cf. A086463 (analog 2-dimensional percolation constant).
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KEYWORD
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AUTHOR
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STATUS
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approved
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