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

%I A092325 #32 Oct 28 2021 02:07:32
%S A092325 3,10,29,69,148,258,430,658,985,1401,1876,2490,3181,3994,4992,6152,
%T A092325 7436,8846,10495,12298,14315,16634,19146,21929,24928,28081,31520,
%U A092325 35347,39514,44131,49146,54134,59500,65176,71349,77684,84540,91757,99341,107404,115863,124728,134223,143944,154316,165265,176936,188764,200743
%N A092325 a(n) = min{ m : sum_{n <= i <= m} 1/p_i > 1}, where p_i is the i-th prime = A000040(i).
%H A092325 Amiram Eldar, <a href="/A092325/b092325.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..85 from Fintan Costello).
%H A092325 Michael Domaratzki, Keith Ellul, Jeffrey Shallit and Ming-Wei Wang, <a href="http://dx.doi.org/10.1142/S0129054105003352">Non-Uniqueness and Radius of Cyclic Unary NFAs</a>, International Journal of Foundations of Computer Science, Vol. 16, No. 5 (2005) pp. 883-896, <a href="http://www.cs.umanitoba.ca/~mdomarat/pubs/DESW_dcfs.pdf">alternative link</a>.
%F A092325 a(n) = A000720(A119494(n)) - _Amiram Eldar_, Dec 24 2018.
%e A092325 a(2) = 10 as 1/3+1/5+1/7+1/11+1/13+1/17+1/19+1/23+1/29 > 1
%e A092325 but 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 < 1 (29 is the 10th prime).
%t A092325 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 *)
%t A092325 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 *)
%Y A092325 Cf. A119494.
%K A092325 nonn
%O A092325 1,1
%A A092325 Michael Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Apr 02 2004
%E A092325 More terms from _Robert G. Wilson v_, Apr 07 2004
%E A092325 More terms from _Fintan Costello_, Jun 03 2011