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A102525
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Decimal expansion of log(2)/log(3).
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18
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6, 3, 0, 9, 2, 9, 7, 5, 3, 5, 7, 1, 4, 5, 7, 4, 3, 7, 0, 9, 9, 5, 2, 7, 1, 1, 4, 3, 4, 2, 7, 6, 0, 8, 5, 4, 2, 9, 9, 5, 8, 5, 6, 4, 0, 1, 3, 1, 8, 8, 0, 4, 2, 7, 8, 7, 0, 6, 5, 4, 9, 4, 3, 8, 3, 8, 6, 8, 5, 2, 0, 1, 3, 8, 0, 9, 1, 4, 8, 0, 5, 0, 6, 1, 1, 7, 2, 6, 8, 8, 5, 4, 9, 4, 5, 1, 7, 4, 5, 5, 6, 1, 3, 5, 4
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OFFSET
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0,1
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COMMENTS
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log_3(2) is the Hausdorff dimension of the Cantor set.
Comment from Stanislav Sykora, Apr 19 2016: Twice this value is the Hausdorff dimension of the Koch curve, as well as of the 2D Cantor dust. Three times its value is the Hausdorff dimension of the Sierpinski carpet, as well as of the 3D Cantor dust. More in general, N times its value is the Hausdorff dimension of N-dimensional Cantor dust. This number is known to be transcendental.
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REFERENCES
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K. J. Falconer, The Geometry of Fractal Sets, Cambridge, 1985, see p. 14.
G. H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, 5th Edition, Oxford University Press, ISBN 978-0198531715, 1979, p. 162.
Nigel Lesmoir-Gordon, Will Rood and Ralph Edney, Introducing Fractal Geometry, Totem Books USA, Lanham, MD, 2001, page 28.
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LINKS
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FORMULA
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EXAMPLE
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log(2)/log(3) = 0.63092975357145743709952711434276085429958564...
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MAPLE
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MATHEMATICA
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RealDigits[Log[3, 2], 10, 111][[1]]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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