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A234364 Primes which are the arithmetic mean of the squares of four consecutive primes.

%I A234364 #14 Oct 08 2014 16:45:35
%S A234364 157,337,673,1213,1777,2137,11677,20773,27259,32803,80407,84787,89227,
%T A234364 105397,120097,165313,176461,181513,250543,417337,453667,463807,
%U A234364 576883,610867,791317,804757,853873,935167,949687,1087903
%N A234364 Primes which are the arithmetic mean of the squares of four consecutive primes.
%H A234364 K. D. Bajpai, <a href="/A234364/b234364.txt">Table of n, a(n) for n = 1..5666</a>
%e A234364 157 is in the sequence because (7^2 + 11^2 + 13^2 + 17^2)/4 = 157 which is prime.
%e A234364 1213 is in the sequence because (29^2 + 31^2 + 37^2 + 41^2)/4 = 1213 which is prime.
%p A234364 KD := proc() local a,b,d,e,f,g; a:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=ithprime(n+3); g:=(a^2+b^2+d^2+e^2)/4; if g=floor(g) and isprime(g) then RETURN (g);  fi;  end: seq(KD(), n=1..500);
%t A234364 Select[Table[Mean[Prime[Range[n, n + 3]]^2], {n, 250}], PrimeQ] (* _Alonso del Arte_, Dec 26 2013 *)
%t A234364 Select[Mean/@(Partition[Prime[Range[200]],4,1]^2),PrimeQ] (* _Harvey P. Dale_, Oct 08 2014 *)
%Y A234364 Cf. A084951: primes of the form (prime(k)^2 + prime(k+1)^2 + prime(k+2)^2)/3.
%Y A234364 Cf. A093343: primes of the form (prime(k)^2 + prime(k+1)^2)/2.
%K A234364 nonn
%O A234364 1,1
%A A234364 _K. D. Bajpai_, Dec 25 2013