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A102525 Decimal expansion of log(2)/log(3). 18
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
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.
REFERENCES
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.
LINKS
Turnbull WWW Server, Felix Hausdorff.
Eric Weisstein's World of Mathematics, Cantor Set
Eric Weisstein's World of Mathematics, Transcendental Number
Wikipedia, Cantor set
Wikipedia, Koch snowflake
FORMULA
Equals A100831 / 2.
Equals 1 / A020857. - Bernard Schott, Feb 02 2023
EXAMPLE
log(2)/log(3) = 0.63092975357145743709952711434276085429958564...
MAPLE
evalf(log(2)/log(3), 100); # Bernard Schott, Feb 02 2023
MATHEMATICA
RealDigits[Log[3, 2], 10, 111][[1]]
PROG
(PARI) log(2)/log(3) \\ Altug Alkan, Apr 19 2016
CROSSREFS
Sequence in context: A191896 A100125 A153459 * A119923 A359194 A204420
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Jan 13 2005
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)