A346640 Decimal expansion of 2 - log_3(2).

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, 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, 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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..105.

Timothy Bedford, Crinkly Curves, Markov Partitions and Dimension, 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).

Curtis T. McMullen, Hausdorff Dimension of General Sierpinski Carpets, 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.

Formula

Equals 2 - A102525.

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

Example

1.3690702464285425629004728856572391...

Mathematica

RealDigits[2 - Log[3, 2], 10, 105][[1]] (* Amiram Eldar, Jul 27 2021 *)

Prog

(PARI) 2 - log(2)/log(3) \\ Michel Marcus, Jul 27 2021

Crossrefs

Cf. A102525, A346639.

Cf. A213201.

Sequence in context: A281802 A197292 A232817 * A247398 A094560 A179615

Adjacent sequences: A346637 A346638 A346639 * A346641 A346642 A346643

Keyword

cons,nonn

Author

Kevin Ryde, Jul 26 2021

Status

approved