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A098062 Primes of the form n^2 + 4n + 8. 3
13, 29, 53, 173, 229, 293, 733, 1093, 1229, 1373, 2029, 2213, 3253, 4229, 4493, 5333, 7229, 7573, 9029, 9413, 10613, 13229, 13693, 15629, 18229, 18773, 21613, 24029, 26573, 27893, 31333, 33493, 37253, 41213, 42853, 46229, 47093, 54293, 55229 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or, primes that are equal to the mean of 7 consecutive squares. - Zak Seidov, Apr 14 2007

Sum of 7 consecutive squares starting with m^2 is equal to 7*(13 + 6*m + m^2) and mean is (13 + 6*m + m^2)=(m+3)^2+4. Hence a(n)=A005473(n+1). Note that only nonnegative m's are considered. - Zak Seidov, Apr 14 2007

a(n)==1 (mod 4).

a(n)= A005473(n+1). - Zak Seidov, Apr 12 2007

LINKS

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

EXAMPLE

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

MATHEMATICA

Select[ Table[ n^2 + 4n + 8, {n, 240}], PrimeQ[ # ] &] (* Robert G. Wilson v, Sep 14 2004 *)

PROG

(PARI) for(n=0, 240, if(isprime(p=n^2+4*n+8), print1(p, ", "))) \\ Klaus Brockhaus

(MAGMA) [a: n in [0..250] | IsPrime(a) where a is n^2 + 4*n + 8]; // Vincenzo Librandi, Jul 17 2012

CROSSREFS

Cf. A005473, A056899, A067201, A007591, A129389, A129412.

Sequence in context: A162579 A286658 A090866 * A094481 A045637 A146743

Adjacent sequences:  A098059 A098060 A098061 * A098063 A098064 A098065

KEYWORD

nonn,easy

AUTHOR

Giovanni Teofilatto, Sep 12 2004

EXTENSIONS

Edited, corrected and extended by Robert G. Wilson v and Klaus Brockhaus, Sep 14 2004

Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified May 22 21:00 EDT 2019. Contains 323497 sequences. (Running on oeis4.)