A100831 -id:A100831

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A102525

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

+10
19

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.

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

Cf. A020857, A100831.

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Jan 13 2005

STATUS

approved

A152566

Decimal expansion of log_3(10).

+10
3

2, 0, 9, 5, 9, 0, 3, 2, 7, 4, 2, 8, 9, 3, 8, 4, 6, 0, 4, 2, 9, 6, 5, 6, 7, 5, 2, 2, 0, 2, 1, 4, 0, 1, 2, 5, 0, 6, 0, 7, 5, 1, 8, 0, 0, 6, 7, 9, 7, 9, 3, 0, 1, 1, 6, 9, 2, 3, 5, 4, 5, 3, 3, 8, 6, 3, 4, 1, 7, 7, 4, 7, 7, 5, 7, 1, 9, 4, 0, 6, 2, 8, 7, 1, 6, 7, 6, 5, 8, 0, 2, 3, 0, 8, 9, 8, 1, 2, 3

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for transcendental numbers

EXAMPLE

2.0959032742893846042965675220214012506075180067979301169235...

MATHEMATICA

RealDigits[Log[3, 10], 10, 120][[1]] (* Vincenzo Librandi, Aug 29 2013 *)

PROG

(PARI) log(10)/log(3) \\ Charles R Greathouse IV, Aug 06 2020

CROSSREFS

Cf. A102524, A100831, A113209, A102525, A152565, A113210, A152566, A152549, A152564.

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Oct 28 2009

STATUS

approved

A102447

Decimal expansion of log_3(20).

+10
2

2, 7, 2, 6, 8, 3, 3, 0, 2, 7, 8, 6, 0, 8, 4, 2, 0, 4, 1, 3, 9, 6, 0, 9, 4, 6, 3, 6, 3, 6, 4, 1, 6, 2, 1, 0, 4, 9, 0, 7, 1, 0, 3, 6, 4, 6, 9, 2, 9, 8, 1, 0, 5, 4, 4, 7, 9, 4, 2, 0, 0, 2, 8, 2, 4, 7, 2, 8, 6, 2, 6, 7, 8, 9, 5, 2, 8, 5, 5, 4, 3, 3, 7, 7, 7, 9, 3, 8, 4, 9, 0, 8, 5, 8, 4, 3, 2, 9, 8, 2, 5, 6, 1, 2, 0

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Hausdorff dimension of Menger sponge.

REFERENCES

Manfred Schroeder, Fractals, Chaos, Power Laws, Freeman,1991, p. 179.

Ian Stewart, Does God Play Dice?, The New Mathematics of Chaos, 2nd Ed., Blackwell Pub'l., Malden MA, 2002, p. 207.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

C. C. Bergemann, PlanetMath.org, Menger sponge

O. Knill, Menger Sponge

School of Mathematics and Statistics, University of St Andrews, Scotland, Abram Samoilovitch Besicovitch.

Turnbull WWW Server, Felix Hausdorff.

Eric Weisstein's World of Mathematics, Menger Sponge

Wikipedia, Hausdorff dimension.

Index entries for transcendental numbers

EXAMPLE

2.72683302786084204139609463636416210490710364692981054479420028247...

MATHEMATICA

RealDigits[ Log[3, 20], 10, 111][[1]]

PROG

(PARI) log(20)/log(3) \\ Michel Marcus, Jul 19 2020

CROSSREFS

Cf. A100831, A102525, A113210, A152564.

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Feb 23 2005

STATUS

approved

A228375

Decimal expansion of log_3(25).

+10
1

2, 9, 2, 9, 9, 4, 7, 0, 4, 1, 4, 3, 5, 8, 5, 4, 3, 3, 4, 3, 9, 4, 0, 8, 0, 8, 1, 5, 3, 5, 7, 2, 8, 0, 7, 9, 2, 6, 1, 5, 8, 6, 4, 7, 3, 3, 3, 3, 2, 0, 9, 9, 3, 7, 8, 1, 0, 5, 7, 8, 0, 7, 8, 9, 5, 9, 0, 9, 8, 4, 5, 5, 2, 3, 8, 2, 0, 5, 1, 6, 4, 7, 3, 1, 1, 1, 8

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for transcendental numbers

FORMULA

Equals 2*A113209. - R. J. Mathar, Sep 08 2013

EXAMPLE

2.92994704143585433439408081535728079261586473333209937810578078959098...

MATHEMATICA

RealDigits[Log[3, 25], 10, 100][[1]]

CROSSREFS

Cf. decimal expansion of log_3(m): A102525 (m=2), A100831 (m=4), A113209 (m=5), A153459 (m=6), A152565 (m=7), A113210 (m=8), A152566 (m=10), A154175 (m=11), A154196 (m=12), A154217 (m=13), A154463 (m=14), A154542 (m=15), A154751 (m=16), A154848 (m=17), A152549 (m=18), A155003 (m=19), A102447 (m=20), A155541 (m=21), A155694 (m=22), A155808 (m=23), A155922 (m=24), this sequence, A152564 (m=26).

KEYWORD

nonn,cons,easy

AUTHOR

Vincenzo Librandi, Aug 29 2013

STATUS

approved

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