A120850 Numbers n such that n is prime and is equal to the sum of the first k primes plus the product of the first k primes, for some k.

11, 227, 30071, 24647906487115793512432470614609487044327490547070674282967249490409801198254927547005559122946385681862066942903289, 62797802135946735863734268232365323600796854989079318289826397214991489160762431714712874321823048719463864215556568570809157897364620234601356930764612312239892910549558645813243759770009793795858849126389709

Offset: 1

Author

Carlos Alves, Jul 08 2006

Keywords

• nonn

Comments

It is in the spirit of A096342 (only for 2 consecutive primes) and of A013918 (all primes but only the sum).

The corresponding values of k are 2, 4, 6, 60, 96, ... - Amiram Eldar, Dec 19 2018

Examples

			11=(2+3)+(2*3) and 11 is prime.
227= (2+3+5+7)+(2*3*5*7) and 227 is prime.
		

Crossrefs

Cf. A096342, A013918, A120851.

Programs

Mathematica

tb = {};Do[pq = Plus @@ Prime[Range[1, k]] + Times @@ Prime[Range[1, k]]; If[PrimeQ[pq], AppendTo[tb, pq]], {k, 1, 200}]; tb