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Search: id:A076751
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| A076751 |
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Sum of 1/k over all composite k in [4..a(n)] is greater than n. |
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+0
1
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| 16, 63, 216, 715, 2279, 7102, 21722, 65558, 195759, 579465, 1703072, 4975222, 14459492, 41837580, 120585504, 346372172, 991915208
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These partial sums, like the harmonic sequence (A004080), can never be integers.
Limit as n -> inf. of a(n+1)/a(n) = e.
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EXAMPLE
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a(1) = 1 because 1/4 + 1/6 + 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/16 =~ 1.0367063492... > 1.
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MATHEMATICA
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NextComposite[n_] := Block[{k = n + 1}, While[ PrimeQ[k], k++ ]; k]; k = 4; s = 0; Do[ While[s = s + 1/k; s < n, k = NextComposite[k]]; Print[k]; k = NextComposite[k], {n, 1, 17}]
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CROSSREFS
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Cf. A004080, A016088.
Sequence in context: A022289 A100176 A060091 this_sequence A090567 A118902 A092210
Adjacent sequences: A076748 A076749 A076750 this_sequence A076752 A076753 A076754
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KEYWORD
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hard,more,nonn
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AUTHOR
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Jack Brennen (jb(AT)brennen.net), Nov 12 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 14 2002
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