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A102525 Decimal expansion of log(2)/log(3). 10
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

Table of n, a(n) for n=0..104.

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, Hausdorff dimension.

Wikipedia, List of fractals by Hausdorff dimension

Wikipedia, Koch snowflake

Wikipedia, Sierpinski carpet

Index entries for transcendental numbers

FORMULA

Equals A100831 / 2.

EXAMPLE

log(2)/log(3) = 0.63092975357145743709952711434276085429958564...

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 A204420 A331570

Adjacent sequences:  A102522 A102523 A102524 * A102526 A102527 A102528

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Jan 13 2005

STATUS

approved

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Last modified October 23 21:23 EDT 2021. Contains 348216 sequences. (Running on oeis4.)