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Search: id:A079937
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| A079937 |
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Greedy frac multiples of Pi^2/6: a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=Pi^2/6. |
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+0
6
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| 1, 2, 14, 45, 107, 138, 276, 414, 1135, 2270, 6672, 12209, 18881, 180865
(list; graph; listen)
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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) = 45 since frac(1x) + frac(2x) + frac(14x) + frac(45x) < 1, while frac(1x) + frac(2x) + frac(14x) + frac(k*x) > 1 for all k>14 and k<45.
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CROSSREFS
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Cf. A080017 (denominators of convergents to Pi^2/6), A079934, A079938, A079939.
Sequence in context: A091405 A085929 A036659 this_sequence A083102 A056080 A163796
Adjacent sequences: A079934 A079935 A079936 this_sequence A079938 A079939 A079940
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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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