

A046024


a(n) = smallest k such that Sum_{ i = 1..k } 1/prime(i) exceeds n.


19




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) 22832305
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



