A279903 Decimal expansion of Hausdorff dimension of E_{1,2}: set of irrationals whose continued fraction expansion consists only of 1's and 2's.

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

Offset

0,1

Links

Andrey Zabolotskiy, Table of n, a(n) for n = 0..199 (from Pollicott & Vytnova)

Oliver Jenkinson, On the density of Hausdorff dimensions of bounded type continued fraction sets: The Texan conjecture, Stoch. Dyn. 04, 63 (2004).

Oliver Jenkinson and Mark Pollicott, Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: a hundred decimal digits for the dimension of E_2, arXiv:1611.09276 [math.DS], 2016.

M. H. Kolkhuis Tanke, Continued fractions with restricted digits and their Hausdorff dimension (bachelor thesis), 2016.

M. Pollicott and P. Vytnova, Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups, Trans. Amer. Math. Soc. Ser. B, 9 (2022), 1102-1159.

J. Thurlby, Rigorous calculations of renormalisation fixed points and attractors, PhD thesis, U. Portsmouth, (2021), eq. (5.42)

Example

dim(E_{1,2}) = 0.531280506277205141624468647368471785493059109018398779...

Crossrefs

Sequence in context: A196613 A151903 A160276 * A309446 A242439 A176318

Adjacent sequences: A279900 A279901 A279902 * A279904 A279905 A279906

Keyword

nonn,cons

Author

Andrey Zabolotskiy, Dec 22 2016

Extensions

More terms from Andrey Zabolotskiy, Aug 08 2017 from Jenkinson & Pollicott, 2016.

Status

approved