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A086773
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Decimal expansion of the continued fraction 1/(Pi+1/(Pi+1/(Pi+1/(Pi+...)))).
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1
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2, 9, 1, 2, 9, 9, 5, 6, 2, 3, 2, 3, 6, 9, 0, 0, 0, 5, 7, 3, 8, 8, 1, 6, 9, 8, 6, 9, 5, 6, 3, 0, 8, 0, 8, 2, 7, 0, 5, 5, 6, 4, 7, 0, 6, 4, 4, 5, 1, 3, 8, 5, 9, 8, 5, 3, 5, 2, 0, 7, 6, 2, 9, 6, 5, 0, 9, 8, 2, 4, 0, 4, 8, 5, 9, 2, 4, 0, 7, 0, 3, 6, 7, 6, 0, 8, 5, 4, 2, 1, 6, 2, 3, 6, 1, 6, 7, 1, 6, 4, 8, 0, 0, 2, 1
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OFFSET
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0,1
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COMMENTS
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Repeat s = s + Pi; s=1/s. The initial value of s is irrelevant.
Solves log(x+Pi) = -log(x). This equation represents the first (by absolute value) self-intersection of the spiral defined by the polar equation r=log(theta), and this constant is the smaller value of theta in the self-intersection. - Jeremy Tan, Sep 03 2016
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LINKS
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FORMULA
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Equals (sqrt(Pi^2+4)-Pi)/2 = 0.2912995... . - R. J. Mathar, Sep 15 2012
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EXAMPLE
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1
------
Pi + 1
------
Pi + 1
--------
Pi + ...
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MATHEMATICA
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RealDigits[N[(Sqrt[Pi^2 + 4] - Pi)/2, 120]] // First (* Michael De Vlieger, Mar 31 2015 *)
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PROG
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(PARI) default(realprecision, 2000); f(n) = s=0; for(x=1, n, s=s+Pi; s=1/s); print(s)
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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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