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Search: id:A092753
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| A092753 |
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a(n) = smallest m >= 1 such that Sum_{k=1..m} log(k)/k >= n. |
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+0
1
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| 1, 4, 8, 12, 17, 24, 33, 43, 56, 71, 89, 111, 136, 166, 201, 242, 290, 345, 408, 481, 565, 660, 768, 892, 1031, 1190, 1368, 1569, 1796, 2049, 2334, 2652, 3008, 3405, 3847, 4339, 4885, 5491, 6162, 6905, 7726, 8634, 9634, 10737, 11951, 13287, 14754, 16364
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum (-1)^k log(k) / k is a conditionally convergent sequence that converges to gamma log(2) - (log 2)^2 / 2. But the sum of the absolute values diverges.
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EXAMPLE
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The sum of the first 4 terms is 1.059351276782648539882313867..., just >= 1, so a(1) = 4.
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MATHEMATICA
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f[n_] := Block[{s = 0, k = 1}, While[s = N[s + Log[k]/k, 128]; s < n, k++ ]; k]; Table[ f[n], {n, 0, 47}] (from Robert G. Wilson v Apr 15 2004)
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CROSSREFS
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Cf. A002387.
Sequence in context: A033156 A036573 A098573 this_sequence A079774 A045672 A072473
Adjacent sequences: A092750 A092751 A092752 this_sequence A092754 A092755 A092756
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Apr 13 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Don Reble (djr(AT)nk.ca), Apr 15 2004
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