A129412 Numbers n such that mean of 7 consecutive squares starting with n^2 is prime.

0, 2, 4, 10, 12, 14, 24, 30, 32, 34, 42, 44, 54, 62, 64, 70, 82, 84, 92, 94, 100, 112, 114, 122, 132, 134, 144, 152, 160, 164, 174, 180, 190, 200, 204, 212, 214, 230, 232, 240, 242, 250, 252, 262, 264, 272, 274, 284, 290, 300, 304, 310, 314, 344, 354, 370, 372

Offset

1,2

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

Select[Range[0, 400], PrimeQ[Mean[Range[#, #+6]^2]]&]  (* Harvey P. Dale, Apr 23 2011 *)

Prog

(PARI) is(n)=isprime(n^2+6*n+13) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A356664 A138940 A278465 * A266115 A113536 A081887

Adjacent sequences: A129409 A129410 A129411 * A129413 A129414 A129415

Keyword

nonn,easy

Author

Zak Seidov, Apr 14 2007

Status

approved