A272408 Decimal expansion of the Hausdorff dimension of the Rauzy fractal boundary.

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

Offset

1,3

Comments

Recipe: find the roots of z^3-z^2-z-1=0. The real one is the tribonacci constant (A058265) and is of no interest here. The other two are complex conjugates; denote their shared magnitude b. Now this constant is the solution of 2*b^(3x)+b^(4x) = 1.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Wikipedia, Rauzy fractal

Example

1.09336416428230663992244770117307346816995623374111426411497299420...

Prog

(PARI) \\ Using 2010 digits realprecision:
b=abs(polroots(Pol([1, -1, -1, -1]))[2]);
a=solve(x=1, 2, 2*b^(3*x)+b^(4*x)-1)

Crossrefs

Cf. A058265.

Sequence in context: A037921 A327135 A019878 * A177910 A198416 A097902

Adjacent sequences: A272405 A272406 A272407 * A272409 A272410 A272411

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Apr 29 2016

Status

approved