|
Search: id:A119494
|
|
|
| A119494 |
|
a(n) = smallest prime number p_k such that 1/p_n+1/p_{n+1}+...+1/p_k > 1. |
|
+0
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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
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.
|
|
FORMULA
|
a(n) is approximately p(n)^e.
|
|
EXAMPLE
|
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.
|
|
PROGRAM
|
(PARI) a(n)=my(s=0.); forprime(p=prime(n), default(primelimit), s+=1/p; if(s>1, return(p)))
|
|
CROSSREFS
|
Cf. A092325, A016088.
Sequence in context: A034700 A057721 A085151 this_sequence A153077 A000352 A034332
Adjacent sequences: A119491 A119492 A119493 this_sequence A119495 A119496 A119497
|
|
KEYWORD
|
nonn,new
|
|
AUTHOR
|
Charles R. Greathouse May 25 2006
|
|
EXTENSIONS
|
Definition corrected by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 09 2006
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 12 2009
|
|
|
Search completed in 0.002 seconds
|
