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A046024
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a(n) = smallest k such that Sum_{ i = 1..k } 1/prime(i) exceeds n.
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22
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OFFSET
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0,2
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COMMENTS
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The corresponding primes prime(a(n)) are in A016088.
Index m for which the prime harmonic number p[ m ] := Sum[ 1/Prime[ k ],{k,1,m} ] >= n.
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LINKS
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Table of n, a(n) for n=0..4.
E. Bach, D. Klyve, J. P. Sorenson, Computing prime harmonic sums, Math. Comp. 78 (2009) 2283-2305
Eric Weisstein's World of Mathematics, Prime Number.
Eric Weisstein's World of Mathematics, Harmonic Series of Primes
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FORMULA
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a(n) = A000720(A016088(n)) = A000720(A096232(n))+1. - Jonathan Sondow, Apr 17 2013
a(n) = e^(e^(n + O(1))), see comment in A223037. - Jonathan Sondow, Apr 17 2013; corrected by Charles R Greathouse IV, Aug 22 2013
a(n) = A103591(2*n). - Michel Marcus, Aug 22 2013
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MATHEMATICA
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Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) <= n, m++];
m, {n, 0, 4}] (* Robert Price, Mar 27 2019 *)
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PROG
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(PARI) a(n)=my(t); forprime(p=2, , t+=1./p; if(t>n, return(p))) \\ Charles R Greathouse IV, Apr 29 2015
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CROSSREFS
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Cf. A004080, A016088, A096232, A223037.
Sequence in context: A185153 A215609 A201184 * A184951 A081853 A183286
Adjacent sequences: A046021 A046022 A046023 * A046025 A046026 A046027
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KEYWORD
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nonn,more,nice
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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a(4) found by Tomás Oliveira e Silva (tos(AT)det.ua.pt), using the fourth term of A016088. - Dec 14 2005
a(0) from Jonathan Sondow, Apr 16 2013
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STATUS
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approved
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