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Search: id:A079941
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| A079941 |
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Greedy frac multiples of ln(2): a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=ln(2). |
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+0
7
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| 1, 3, 6, 13, 26, 39, 277, 642, 2291, 4582, 6231, 16402, 26573, 36744, 63317, 73488, 110232, 414355, 828710
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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) = 13 since frac(1x) + frac(3x) + frac(6x) + frac(13x) < 1, while frac(1x) + frac(3x) + frac(6x) + frac(k*x) > 1 for all k>6 and k<13.
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CROSSREFS
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Cf. A079943 (denominators of convergents to ln2), A079934, A079939, A079940.
Sequence in context: A121349 A074890 A032198 this_sequence A019300 A072762 A081254
Adjacent sequences: A079938 A079939 A079940 this_sequence A079942 A079943 A079944
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KEYWORD
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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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More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003
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