This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102525 #31 Feb 16 2025 08:32:56 %S A102525 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, %T A102525 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, %U A102525 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 %N A102525 Decimal expansion of log(2)/log(3). %C A102525 log_3(2) is the Hausdorff dimension of the Cantor set. %C A102525 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. %D A102525 K. J. Falconer, The Geometry of Fractal Sets, Cambridge, 1985, see p. 14. %D A102525 G. H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, 5th Edition, Oxford University Press, ISBN 978-0198531715, 1979, p. 162. %D A102525 Nigel Lesmoir-Gordon, Will Rood and Ralph Edney, Introducing Fractal Geometry, Totem Books USA, Lanham, MD, 2001, page 28. %H A102525 Turnbull WWW Server, <a href="http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hausdorff.html">Felix Hausdorff</a>. %H A102525 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CantorSet.html">Cantor Set</a> %H A102525 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TranscendentalNumber.html">Transcendental Number</a> %H A102525 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cantor_set">Cantor set</a> %H A102525 Wikipedia, <a href="http://en.wikipedia.org/wiki/Hausdorff_dimension">Hausdorff dimension</a>. %H A102525 Wikipedia, <a href="http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension">List of fractals by Hausdorff dimension</a> %H A102525 Wikipedia, <a href="http://en.wikipedia.org/wiki/Koch_snowflake">Koch snowflake</a> %H A102525 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sierpinski_carpet">Sierpinski carpet</a> %H A102525 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A102525 Equals A100831 / 2. %F A102525 Equals 1 / A020857. - _Bernard Schott_, Feb 02 2023 %e A102525 log(2)/log(3) = 0.63092975357145743709952711434276085429958564... %p A102525 evalf(log(2)/log(3),100); # _Bernard Schott_, Feb 02 2023 %t A102525 RealDigits[Log[3, 2], 10, 111][[1]] %o A102525 (PARI) log(2)/log(3) \\ _Altug Alkan_, Apr 19 2016 %Y A102525 Cf. A020857, A100831. %K A102525 cons,nonn %O A102525 0,1 %A A102525 _Robert G. Wilson v_, Jan 13 2005