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A234432 Primes which are the arithmetic mean of the squares of six consecutive primes. 1

%I

%S 9413,25673,38237,43573,81553,106453,136273,145513,257857,294013,

%T 325753,430433,497257,599273,702413,907733,948173,1238893,2053553,

%U 2185577,2883457,3972113,4226077,4375177,4494577,4728313,6106141

%N Primes which are the arithmetic mean of the squares of six consecutive primes.

%H K. D. Bajpai, <a href="/A234432/b234432.txt">Table of n, a(n) for n = 1..8250</a>

%e 9413 is in the sequence because (83^2 + 89^2 + 97^2 + 101^2 + 103^2 + 107^2)/6 = 9413 which is prime.

%e 25673 is in the sequence because (149^2 + 151^2 + 157^2 + 163^2 + 167^2 + 173^2)/6 = 25673 which is prime.

%p KD := proc() local a,b,d,e,f,g,h; a:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=ithprime(n+3); f:=ithprime(n+4);h:=ithprime(n+5); g:=(a^2+b^2+d^2+e^2+f^2+h^2)/6; if g=floor(g) and isprime(g) then RETURN (g); fi; end: seq(KD(), n=2..1000);

%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 26 2013

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Last modified May 13 23:41 EDT 2021. Contains 343868 sequences. (Running on oeis4.)