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

1,1

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.

Formula

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

Example

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).

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 *)

Crossrefs

Cf. A119494.

Sequence in context: A350821 A361741 A055336 * A130218 A114958 A048493

Adjacent sequences: A092322 A092323 A092324 * A092326 A092327 A092328

Keyword

nonn

Author

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

Extensions

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

More terms from Fintan Costello, Jun 03 2011

Status

approved