A046024 - OEIS (original) (raw)

A046024

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

22

1, 3, 59, 361139, 43922730588128390

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.

MATHEMATICA

Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) <= n, m++];

PROG

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

EXTENSIONS

a(4) found by Tomás Oliveira e Silva (tos(AT)det.ua.pt), using the fourth term of A016088. - Dec 14 2005