

A102525


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


9



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 Ndimensional 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 9780198531715, 1979, p. 162.
Nigel LesmoirGordon, 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, The Free Encyclopedia, Cantor set
Wikipedia, The Free Encyclopedia, Hausdorff dimension.
Wikipedia, The Free Encyclopedia, List of fractals by Hausdorff dimension
Wikipedia, The Free Encyclopedia, Koch snowflake
Wikipedia, The Free Encyclopedia, Sierpinski carpet


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 A102410
Adjacent sequences: A102522 A102523 A102524 * A102526 A102527 A102528


KEYWORD

cons,nonn


AUTHOR

Robert G. Wilson v, Jan 13 2005


STATUS

approved



