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A234364
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Primes which are the arithmetic mean of the squares of four consecutive primes.
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1
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157, 337, 673, 1213, 1777, 2137, 11677, 20773, 27259, 32803, 80407, 84787, 89227, 105397, 120097, 165313, 176461, 181513, 250543, 417337, 453667, 463807, 576883, 610867, 791317, 804757, 853873, 935167, 949687, 1087903
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OFFSET
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1,1
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LINKS
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EXAMPLE
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157 is in the sequence because (7^2 + 11^2 + 13^2 + 17^2)/4 = 157 which is prime.
1213 is in the sequence because (29^2 + 31^2 + 37^2 + 41^2)/4 = 1213 which is prime.
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MAPLE
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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);
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MATHEMATICA
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Select[Table[Mean[Prime[Range[n, n + 3]]^2], {n, 250}], PrimeQ] (* Alonso del Arte, Dec 26 2013 *)
Select[Mean/@(Partition[Prime[Range[200]], 4, 1]^2), PrimeQ] (* Harvey P. Dale, Oct 08 2014 *)
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CROSSREFS
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Cf. A084951: primes of the form (prime(k)^2 + prime(k+1)^2 + prime(k+2)^2)/3.
Cf. A093343: primes of the form (prime(k)^2 + prime(k+1)^2)/2.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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