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%I #17 Aug 01 2020 19:32:53
%S 2723401,13036537,52774873,78972121,116515177,123179113,235236049,
%T 242120017,834990721,850037521,943067353,943804801,1302156313,
%U 1582432681,1659047497,1830419449,1999538809,2025774697,2609800657
%N Primes which are the arithmetic mean of the squares of five consecutive primes.
%H K. D. Bajpai, <a href="/A234370/b234370.txt">Table of n, a(n) for n = 1..3270</a>
%e 2723401 is in the sequence because (1627^2 + 1637^2 + 1657^2 + 1663^2 + 1667^2)/5 = 2723401 which is prime.
%e 52774873 is in the sequence because (7243^2 + 7247^2 + 7253^2 + 7283^2 + 7297^2)/5 = 52774873 which is prime.
%p KD := proc() local a,b,d,e,f,g; a:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=ithprime(n+3); f:=ithprime(n+4); g:=(a^2+b^2+d^2+e^2+f^2)/5; if g=floor(g) and isprime(g) then RETURN (g); fi; end: seq(KD(), n=1..10000);
%t Select[Mean/@Partition[Prime[Range[6000]]^2,5,1],PrimeQ] (* _Harvey P. Dale_, Aug 01 2020 *)
%Y Cf. A084951: primes of the form (prime(k)^2 + prime(k+1)^2 + prime(k+2)^2)/3.
%Y Cf. A093343: primes of the form (prime(k)^2 + prime(k+1)^2)/2.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Dec 25 2013
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