A238301 Decimal expansion of Roth number xi(3), a transcendental number based on the Fibonacci sequence.

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

Offset

0,1

Comments

Roth number xi(2) is the rabbit constant, also a transcendental number based on the Fibonacci sequence.

Links

Table of n, a(n) for n=0..105.

D. E. Knuth, Transcendental numbers based on the Fibonacci sequence.

Eric Weisstein's MathWorld, Roth's theorem.

Eric Weisstein's MathWorld, Rabbit Constant.

Index entries for transcendental numbers

Formula

Continued fraction 1/(3^F0 + 1/(3^F1 + 1/(3^F2 + ...))).

Example

0.768597560593155...

Mathematica

digits = 106; dm = 10; Clear[xi]; xi[b_, m_] := xi[b, m] = RealDigits[ ContinuedFractionK[1, b^Fibonacci[k], {k, 0, m}], 10, digits] // First; xi[3, dm]; xi[3, m = 2 dm]; While[xi[3, m] != xi[3, m - dm], m = m + dm]; xi[3, m] (* Mar 04 2015 - update for versions 7 and up, after advice from Oleg Marichev *)

Crossrefs

Cf. A014565.

Sequence in context: A196913 A091343 A196397 * A154170 A308041 A256685

Adjacent sequences: A238298 A238299 A238300 * A238302 A238303 A238304

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 24 2014

Extensions

Corrected and edited by Jean-François Alcover, Mar 04 2015

Status

approved