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A238301
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Decimal expansion of Roth number xi(3), a transcendental number based on the Fibonacci sequence.
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0
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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
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0,1
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COMMENTS
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Roth number xi(2) is the rabbit constant, also a transcendental number based on the Fibonacci sequence.
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LINKS
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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
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FORMULA
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Continued fraction 1/(3^F0 + 1/(3^F1 + 1/(3^F2 + ...))).
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EXAMPLE
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0.768597560593155...
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A014565.
Sequence in context: A196913 A091343 A196397 * A154170 A308041 A256685
Adjacent sequences: A238298 A238299 A238300 * A238302 A238303 A238304
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KEYWORD
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nonn,cons
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AUTHOR
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Jean-François Alcover, Feb 24 2014
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EXTENSIONS
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Corrected and edited by Jean-François Alcover, Mar 04 2015
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STATUS
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approved
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