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 A119494 a(n) = smallest prime number p_k such that 1/p_n+1/p_{n+1}+...+1/p_k > 1. 0

%I

%S 5,29,109,347,857,1627,2999,4931,7759,11677,16111,22229,29269,37717,

%T 48527,61057,75503,91463,110567,131671,155509,183587,214189,248597,

%U 286073,325889,369983,419459,473659,534043,600631,667547,739549,816779

%N a(n) = smallest prime number p_k such that 1/p_n+1/p_{n+1}+...+1/p_k > 1.

%D 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.

%F a(n) is approximately p(n)^e.

%e a(2) = 29 because 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 + 1/29 = 1.0334... > 1 and 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 = 0.9989... < 1.

%o (PARI) a(n)=my(s=0.);forprime(p=prime(n),default(primelimit),s+=1/p;if(s>1,return(p)))

%Y Cf. A092325, A016088.

%K nonn

%O 1,1

%A Charles R. Greathouse May 25 2006

%E Definition corrected by _Ray Chandler_, Jun 09 2006

%E Edited by _Charles R Greathouse IV_, Nov 12 2009

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