

A092325


a(n) = min{ m : sum_{n <= i <= m} 1/p_i > 1}, where p_i is the ith 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
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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 MingWei Wang, NonUniqueness and Radius of Cyclic Unary NFAs, International Journal of Foundations of Computer Science, Vol. 16, No. 5 (2005) pp. 883896, 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 *)


CROSSREFS

Cf. A119494.
Sequence in context: A260811 A108912 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



