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Search: id:A079938
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| A079938 |
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Greedy frac multiples of Pi: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=Pi. |
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5
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OFFSET
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1,2
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COMMENT
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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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EXAMPLE
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a(4) = 8 since frac(1x) + frac(2x) + frac(3x) + frac(8x) < 1, while frac(1x) + frac(2x) + frac(3x) + 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: A003096 A042815 A005008 this_sequence A112237 A132502 A113840
Adjacent sequences: A079935 A079936 A079937 this_sequence A079939 A079940 A079941
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KEYWORD
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more,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), 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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