A126096 Primes that are the arithmetic mean of four successive primes.

127, 139, 149, 181, 241, 431, 967, 1021, 1031, 1061, 1597, 1759, 1913, 2113, 2437, 2593, 2833, 2953, 3769, 3793, 3947, 4219, 4261, 4463, 4603, 5011, 5869, 5923, 6449, 6701, 6959, 7103, 7489, 7549, 7727, 8273, 8803, 8839, 9137, 9241, 9421, 9931, 10069

Offset: 1

Author

Zak Seidov, Mar 03 2007

Keywords

• nonn

Examples

			181 is in the sequence because it is prime and is the arithmetic mean of the consecutive primes 173, 179, 181 and 191.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A102655 (numbers that are the arithmetic mean of four successive primes).

Programs

Maple

a:=proc(n) local nn: nn:=(ithprime(n)+ithprime(n+1)+ithprime(n+2)+ithprime(n+3))/4: if type(nn,integer)=true and isprime(nn)=true then nn else fi end: seq(a(n),n=1..1300); # Emeric Deutsch, Mar 07 2007

Mathematica

lst={};Do[If[PrimeQ[p=(Prime[n]+Prime[n+1]+Prime[n+2]+Prime[n+3])/4],AppendTo[lst,p]],{n,8!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 28 2009 *)
pr=Prime[Range[114000(* for first 3015 terms *)]];
Select[Mean/@Partition[pr,4,1],PrimeQ] (* Zak Seidov, Apr 22 2011 *)

Extensions

More terms from Emeric Deutsch, Mar 07 2007