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Numbers n such that mean of 7 consecutive squares starting with n^2 is prime.
2

%I #9 Jun 13 2017 15:59:54

%S 0,2,4,10,12,14,24,30,32,34,42,44,54,62,64,70,82,84,92,94,100,112,114,

%T 122,132,134,144,152,160,164,174,180,190,200,204,212,214,230,232,240,

%U 242,250,252,262,264,272,274,284,290,300,304,310,314,344,354,370,372

%N Numbers n such that mean of 7 consecutive squares starting with n^2 is prime.

%C Sum of 7 consecutive squares starting with n^2 is equal to 7*(13 + 6*n + n^2) and mean is (13 + 6*n + n^2)=(n+3)^2+4. Hence a(n)=A007591(n+1)-3

%H Charles R Greathouse IV, <a href="/A129412/b129412.txt">Table of n, a(n) for n = 1..10000</a>

%e (0^2+...+6^2)/7=13 prime, (2^2+...+8^2)/7=29 prime, (4^2+...+10^2)/7=53 prime.

%t Select[Range[0,400],PrimeQ[Mean[Range[#,#+6]^2]]&] (* _Harvey P. Dale_, Apr 23 2011 *)

%o (PARI) is(n)=isprime(n^2+6*n+13) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A005473, A056899, A067201, A007591, A129389, A098062.

%K nonn,easy

%O 1,2

%A _Zak Seidov_, Apr 14 2007