A102525 - OEIS

A102525

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

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

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