A129388 Primes that are equal to the mean of 5 consecutive squares.

11, 83, 227, 443, 1091, 1523, 2027, 3251, 6563, 9803, 11027, 12323, 13691, 15131, 21611, 29243, 47963, 50627, 56171, 59051, 62003, 65027, 74531, 88211, 91811, 95483, 103043, 119027, 123203, 131771, 136163, 140627, 149771, 173891, 178931

Offset: 1

Author

Zak Seidov, Apr 12 2007

Keywords

• nonn
• easy

Comments

The sum of 5 consecutive squares starting with k^2 is equal to 5*(6 + 4*k + k^2) and the mean is (6 + 4*k + k^2) = (k+2)^2 + 2. Hence a(n)= A056899(n+2).

Examples

			11 = (1^2 + ... + 5^2)/5;
83 = (7^2 + ... + 11^2)/5;
227 = (13^2 + ... + 17^2)/5.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A056899, A067201, A102305, A129389.

Programs

Magma

[a: n in [1..600] | IsPrime(a) where a is  n^2 + 2*n + 3 ]; // Vincenzo Librandi, Mar 22 2013

Mathematica

Select[Table[n^2 + 2 n + 3, {n, 1, 600}], PrimeQ] (* Vincenzo Librandi, Mar 22 2013 *)

SageMath

A102305=[n^2+2*n+3 for n in range(1,1001)]
[n^2+2*n+3 for n in (1..600) if is_prime(A102305[n-1])] # G. C. Greubel, Feb 03 2024