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A223037
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a(n) = largest prime p such that Sum_{primes q = 2, ..., p} 1/q does not exceed n.
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3
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OFFSET
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1,1
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COMMENTS
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Since Sum_{prime q} 1/q diverges, the sequence is infinite.
In fact, by the Prime Number Theorem Prime(k) ~ k log k as k -> infinity, and by integration Sum_{k <= n} 1/(k log k) ~ log log n, so a(n) ~ Prime(Floor(e^e^n)).
a(4) = A000040(A046024(4)-1) = Prime[43922730588128389], but Mathematica 7.0.0 cannot compute this prime on a Mac computer running OS X.
Instead, using a(4) = largest prime < A016088(4) = 1801241230056600523, Mathematica's PrimeQ function finds that a(4) = 1801241230056600467.
See A016088 for other relevant comments, references, links, and programs.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 3 because 1/2 + 1/3 < 1 < 1/2 + 1/3 + 1/5.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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