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%I #14 Jan 22 2015 01:26:29
%S 127,139,149,181,241,431,967,1021,1031,1061,1597,1759,1913,2113,2437,
%T 2593,2833,2953,3769,3793,3947,4219,4261,4463,4603,5011,5869,5923,
%U 6449,6701,6959,7103,7489,7549,7727,8273,8803,8839,9137,9241,9421,9931,10069
%N Primes that are the arithmetic mean of four successive primes.
%H Zak Seidov, <a href="/A126096/b126096.txt">Table of n, a(n) for n = 1..3000</a>
%e 181 is in the sequence because it is prime and is the arithmetic mean of the consecutive primes 173, 179, 181 and 191.
%p 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
%t 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 *)
%t pr=Prime[Range[114000(* for first 3015 terms *)]];
%t Select[Mean/@Partition[pr,4,1],PrimeQ] (* _Zak Seidov_, Apr 22 2011 *)
%Y Cf. A102655 (numbers that are the arithmetic mean of four successive primes).
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 03 2007
%E More terms from _Emeric Deutsch_, Mar 07 2007
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