A103599 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/6.

1, 1, 1, 2, 2, 3, 4, 6, 10, 16, 29, 59, 140, 400, 1413, 6467, 40261, 361139, 4990906, 114916199, 4833601540

Offset: 1

Author

James R. Buddenhagen, Mar 28 2005

Keywords

• nonn

Comments

a(22) > 5*10^10. - Robert Price, Dec 10 2013

Crossrefs

Cf. A016088, A046024, A103591-A103600.

Programs

Mathematica

For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/6, Print[k]; Break[]]]] (* Robert Price, Dec 09 2013 *)
Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/6, m++];
m, {n, 1, 17}] (* Robert Price, Mar 27 2019 *)

Extensions

a(2)-a(4) and a(19)-a(21) added by Robert Price, Dec 10 2013