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Decimal expansion of 2 - log_3(2).
2

%I #16 Dec 25 2022 14:00:15

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

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

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

%N Decimal expansion of 2 - log_3(2).

%C Bedford and McMullen show this is the metric dimension of Hironaka's curve and equivalent carpets (see A346639).

%H Timothy Bedford, <a href="http://wrap.warwick.ac.uk/50539/">Crinkly Curves, Markov Partitions and Dimension</a>, Ph.D. thesis, University of Warwick, 1984, see proposition 4.1, page 89, cap(E) for the case s=2, t=2, r=3, Sum(k_i)=3 (and noting log(t) is a multiplier, not an exponent).

%H Curtis T. McMullen, <a href="https://doi.org/10.1017/S0027763000021085">Hausdorff Dimension of General Sierpinski Carpets</a>, Nagoya Mathematical Journal, volume 96, number 19, 1984, pages 1-9, see page 2, m.dim(R) for the case m = s = 2 and n = r = 3.

%F Equals 2 - A102525.

%F Equals Sum_{d=1..2} d*log(1+1/d)/log(3). Compare with A213201. - _Michel Marcus_, Dec 25 2022

%e 1.3690702464285425629004728856572391...

%t RealDigits[2 - Log[3, 2], 10, 105][[1]] (* _Amiram Eldar_, Jul 27 2021 *)

%o (PARI) 2 - log(2)/log(3) \\ _Michel Marcus_, Jul 27 2021

%Y Cf. A102525, A346639.

%Y Cf. A213201.

%K cons,nonn

%O 1,2

%A _Kevin Ryde_, Jul 26 2021