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A129388 Primes that are equal to the mean of 5 consecutive squares. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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).
LINKS
EXAMPLE
11 = (1^2 + ... + 5^2)/5;
83 = (7^2 + ... + 11^2)/5;
227 = (13^2 + ... + 17^2)/5.
MATHEMATICA
Select[Table[n^2 + 2 n + 3, {n, 1, 600}], PrimeQ] (* Vincenzo Librandi, Mar 22 2013 *)
PROG
(Magma) [a: n in [1..600] | IsPrime(a) where a is n^2 + 2*n + 3 ]; // 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
CROSSREFS
Sequence in context: A026871 A123367 A177142 * A030692 A294831 A055369
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Apr 12 2007
STATUS
approved

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Last modified June 17 18:36 EDT 2024. Contains 373463 sequences. (Running on oeis4.)