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A272408
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Decimal expansion of the Hausdorff dimension of the Rauzy fractal boundary.
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1
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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1.09336416428230663992244770117307346816995623374111426411497299420...
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PROG
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(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)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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