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Search: id:A096580
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| A096580 |
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a(n) = smallest m >= 2 such that Sum_{k=2..m} 1/(k*log(k)) >= n. |
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+0
9
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OFFSET
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0,1
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COMMENT
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The sum diverges (see reference), so a(n) is well-defined.
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REFERENCES
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M. Goar, Olivier and Abel on series convergence: An episode from early 19th century analysis, Math. Mag., 72 (No. 5, 1999), 347-355.
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LINKS
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Charles R Greathouse IV, Home Page [in lieu of email address]
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FORMULA
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Since Integral 1/(x*log(x)) dx = log log x, a(n) is close to e^(e^n) (cf. A096232, A096404, A016066).
a(n) is roughly exp(exp(n-k)), where k = 0.7946786454... - Charles R Greathouse IV Jul 23 2007
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EXAMPLE
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For m = 27 the sum is 1.992912323604..., for m = 28 it is 2.0036302389..., so a(2) = 28.
For m = 8717 the sum is 2.999991290360..., for m = 8718 it is 3.0000039326..., so a(3) = 8718.
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CROSSREFS
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Cf. A016088.
Sequence in context: A052848 A126266 A003017 this_sequence A028868 A081332 A106868
Adjacent sequences: A096577 A096578 A096579 this_sequence A096581 A096582 A096583
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Aug 13 2004
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EXTENSIONS
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8718 from Robert G. Wilson v, Aug 17 2004
a(4) from Charles R Greathouse IV, Jul 23 2007
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