A092325 a(n) = min{ m : sum_{n <= i <= m} 1/p_i > 1}, where p_i is the i-th prime = A000040(i).

3, 10, 29, 69, 148, 258, 430, 658, 985, 1401, 1876, 2490, 3181, 3994, 4992, 6152, 7436, 8846, 10495, 12298, 14315, 16634, 19146, 21929, 24928, 28081, 31520, 35347, 39514, 44131, 49146, 54134, 59500, 65176, 71349, 77684, 84540, 91757, 99341, 107404, 115863, 124728, 134223, 143944, 154316, 165265, 176936, 188764, 200743

Offset: 1

Author

Michael Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Apr 02 2004

Keywords

• nonn

Examples

			a(2) = 10 as 1/3+1/5+1/7+1/11+1/13+1/17+1/19+1/23+1/29 > 1
but 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 < 1 (29 is the 10th prime).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..85 from Fintan Costello).
• Michael Domaratzki, Keith Ellul, Jeffrey Shallit and Ming-Wei Wang, Non-Uniqueness and Radius of Cyclic Unary NFAs, International Journal of Foundations of Computer Science, Vol. 16, No. 5 (2005) pp. 883-896, alternative link.

Crossrefs

Cf. A119494.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{k = n, p = Prime[n], s = 1/Prime[n]}, While[s < 1, p = NextPrim[p]; s = N[s + 1/p, 64]; k++ ]; k]; Table[ f[n], {n, 41}] (* Robert G. Wilson v, Apr 07 2004 *)
s = 0; j = 1; t1 = Table[While[s <= 1, s = s + 1/Prime[j]; j++]; s = s - 1/Prime[i]; j - 1, {i, 25}]  (* Horst H. Manninger, Oct 11 2021 *)

Formula

a(n) = A000720(A119494(n)) - Amiram Eldar, Dec 24 2018.

Extensions

More terms from Robert G. Wilson v, Apr 07 2004

More terms from Fintan Costello, Jun 03 2011