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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).
2
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
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