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A046024 a(n) = smallest k such that Sum_{ i = 1..k } 1/prime(i) exceeds n. 20
1, 3, 59, 361139, 43922730588128390 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

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

FORMULA

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

PROG

(PARI) a(n)=my(t); forprime(p=2, , t+=1./p; if(t>n, return(p))) \\ Charles R Greathouse IV, Apr 29 2015

CROSSREFS

Cf. A004080, A016088, A096232, A223037.

Sequence in context: A185153 A215609 A201184 * A184951 A081853 A183286

Adjacent sequences:  A046021 A046022 A046023 * A046025 A046026 A046027

KEYWORD

nonn,more,nice

AUTHOR

Eric W. Weisstein

EXTENSIONS

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

STATUS

approved

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Last modified December 4 21:51 EST 2016. Contains 278755 sequences.