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

5, 29, 109, 347, 857, 1627, 2999, 4931, 7759, 11677, 16111, 22229, 29269, 37717, 48527, 61057, 75503, 91463, 110567, 131671, 155509, 183587, 214189, 248597, 286073, 325889, 369983, 419459, 473659, 534043, 600631, 667547, 739549, 816779, 901007, 988661

Offset: 1

Author

Charles R Greathouse IV, May 25 2006

Keywords

• nonn

Comments

Domaratzki, Ellul, Shallit, & Wang call the n-th term of A092325 ϖ(n), and A092325(n) = pi(a(n)). - Charles R Greathouse IV, Aug 08 2016

Examples

			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.
		

References

• J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 76, entry 347 and page 108, entry 857.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• 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.

Crossrefs

Cf. A092325, A016088.

Programs

Mathematica

f[0]={0,0}; f[n_] := f[n] = Module[{f1=f[n-1]}, p=f1[[1]]; s=f1[[2]]-If[n>1, 1/Prime[n-1], 0]; While[s<1, p=NextPrime[p]; s+=1/p]; {p,s}]; f[#][[1]] & /@ Range[30] (* Amiram Eldar, Dec 24 2018 *)

PARI

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

Formula

a(n) is approximately prime(n)^e.

a(n) = prime(A092325(n)). - Amiram Eldar, Dec 24 2018

Extensions

Definition corrected by Ray Chandler, Jun 09 2006

Edited by Charles R Greathouse IV, Nov 12 2009

a(35)-a(36) from Amiram Eldar, Dec 24 2018