A103593 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/3.

1, 2, 3, 6, 16, 59, 400, 6467, 361139, 114916199

Offset: 1

Author

James R. Buddenhagen, Mar 28 2005

Keywords

• nonn
• more

Comments

a(n) <= e^(e^(n/3)), therefore a(10) < 1492725701441. - Stefan Steinerberger, Mar 18 2006

a(11) > 5*10^10. - Robert Price, Dec 10 2013

Links

• Eric Weisstein's World of Mathematics, Harmonic Series of Primes

Crossrefs

Cf. A016088, A046024, A103591-A103600.

Programs

Mathematica

Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/3, m++];
m, {n, 1, 10}] (* Robert Price, Mar 27 2019 *)

Extensions

a(10) from Robert Price, Dec 10 2013