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A079938
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Greedy frac multiples of Pi: a(1)=1, Sum_{n>=1} frac(a(n)*x) = 1 at x = Pi.
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4
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OFFSET
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1,2
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COMMENTS
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The n-th greedy frac multiple of x is the smallest integer that does not cause Sum_{k=1..n} frac(a(k)*x) to exceed unity; an infinite number of terms appear as the denominators of the convergents to the continued fraction of x.
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LINKS
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Table of n, a(n) for n=1..9.
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EXAMPLE
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a(4) = 8 since frac(1x*) + frac(2*x) + frac(3*x) + frac(8*x) < 1, while frac(1*x) + frac(2*x) + frac(3*x) + frac(k*x) > 1 for all k > 3 and k < 8.
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MAPLE
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Digits := 100: a := []: s := 0: x := Pi: for n from 1 to 10000000 do: temp := evalf(s+frac(n*x)): if (temp<1.0) then a := [op(a), n]: print(n): s := s+evalf(frac(n*x)): fi: od: a;
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CROSSREFS
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Cf. A002486 (denominators of convergents to Pi), A079934, A079937, A079939.
Sequence in context: A319218 A243954 A005008 * A324006 A112237 A132502
Adjacent sequences: A079935 A079936 A079937 * A079939 A079940 A079941
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KEYWORD
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more,nonn,changed
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AUTHOR
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Benoit Cloitre and Paul D. Hanna, Jan 21 2003
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EXTENSIONS
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One more term from Mark Hudson, Jan 30 2003
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STATUS
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approved
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