

A238301


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


0



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
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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

JeanFrançois Alcover, Feb 24 2014


EXTENSIONS

Corrected and edited by JeanFrançois Alcover, Mar 04 2015


STATUS

approved



