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A273918
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Numerator of z(n), where z(n) = z(n - 1)^2 + 1/4 and z(0) = 1.
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0
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OFFSET
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0,2
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COMMENTS
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a(8) is approximately 5.698 * 10^93.
The denominator of z(n) is 2^(2^n) for n > 0.
Given that the iteration of z(n) escapes to infinity, this shows that 1 is not in the Julia set for the function z^2 + 1/4. This is of course also true of -1.
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LINKS
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EXAMPLE
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1^2 + 1/4 = 5/4, hence a(1) = 5.
(5/4)^2 + 1/4 = 25/16 + 4/16 = 29/16, hence a(2) = 29.
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MATHEMATICA
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Numerator[NestList[#^2 + 1/4 &, 1, 8]]
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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