A279903 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

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

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

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...