A092965 Greatest prime arising as the product of numbers chosen from among the first n numbers + 1.

2, 3, 7, 13, 61, 241, 2521, 20161, 72577, 604801, 39916801, 59875201, 3113510401, 17435658241, 186810624001, 10461394944001, 118562476032001, 246245142528001, 24329020081766401, 304112751022080001

Offset: 1

Author

Amarnath Murthy, Mar 26 2004

Keywords

• nonn

Comments

There are a maximum of 2^n numbers which arise as the products of the subsets of the first n natural numbers. The actual number is smaller because of repetitions. Then a(n) = the greatest prime obtained on adding 1 to each of these numbers.

Different from A089136 (see the comments there).

Examples

			a(5) = 61 = 3*4*5 + 1. 5! + 1, 4!+ 1, are composite and 2*4*5 + 1 = 41 <61, etc.
		

Links

• Martin Fuller, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A060957, A092967.

Programs

Mathematica

Do[l = Map[Times @@ #&, Subsets[Range[n]]]; Print[Max[Select[Map[ #+1&, l], PrimeQ]]], {n, 20}] (* Ryan Propper, Aug 13 2005 *)
f[n_] := Max@ Select[ Union[ Times @@@ Subsets@ Range@ n] + 1, PrimeQ]; Array[f, 20] (* Robert G. Wilson v, Nov 13 2014 *)

Extensions

More terms from Ryan Propper, Aug 13 2005