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A069139
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Egyptian fraction for square root of 1/2.
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26
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = ceiling(1/(1/sqrt(2) - Sum_{i=0..n-1} 1/a(i))).
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EXAMPLE
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a(3) = 68575 since sqrt(1/2) = 0.707106781186..., 1/2 + 1/5 + 1/141 + 1/68574 = 0.707106781368... (which is too much) and 1/2 + 1/5 + 1/141 + 1/68575 = 0.707106781155... (which is not too much).
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MATHEMATICA
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a = {}; k = N[1/Sqrt[2], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (* Artur Jasinski, Sep 22 2008 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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