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A074631
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a(n) is the smallest k such that the sum of the first k terms of the composite-harmonic series, Sum 1/(j-th composite), is > n.
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5
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9, 44, 168, 587, 1940, 6192, 19285, 59010, 178122, 531923, 1574706, 4628338, 13521477, 39299115, 113712434, 327752962, 941457955
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = Min { k : Sum_{j=1..k} 1/A002808(j) > n }.
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EXAMPLE
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1/4 + 1/6 + 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/16 = 1045/1008, but if 1/16 is not present, the sum is less than 1; 16 is the ninth composite number, so a(1) = 9.
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MATHEMATICA
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NextComposite[n_] := Block[{k = n + 1}, While[PrimeQ[k], k++ ]; k]; s=0; k = 4; Do[While[s = s + 1/k; s < n, k = NextComposite[k]]; Print[k - PrimePi[k] - 1]; k = NextComposite[k], {n, 1, 20}]
Table[Position[Accumulate[1/Select[Range[5*10^6], CompositeQ]], _?(#>n&), 1, 1], {n, 12}]//Flatten (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jan 22 2023 *)
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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