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A005471 Primes of form n^2 + 3n + 9, where n can be positive or negative.
(Formerly M4345)
14
7, 13, 19, 37, 79, 97, 139, 163, 313, 349, 607, 709, 877, 937, 1063, 1129, 1489, 1567, 1987, 2557, 2659, 3313, 3547, 4297, 5119, 5557, 7489, 8017, 8563, 9127, 9319, 9907, 10513, 11779, 12889, 15013, 15259, 16519, 17299, 18097, 18367, 18913, 20029 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms == 1 mod 6. [Zak Seidov, Mar 20 2010]

REFERENCES

S. Barbero, U. Cerruti, N. Murru, M. Abrate, Identities Involving Zeros of Ramanujan and Shanks Cubic Polynomials, Journal of Integer Sequences, 16 (2013), #13.8.1.

Hyun Kwang Kim and Jung Soo Kim, Evaluation of zeta function of the simplest cubic field at negative odd integers, Math. Comp. 71 (2002), no. 239, 1243-1262.

D. Shanks, The simplest cubic fields, Math. Comp., 28 (1974), 1137-1152.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

EXAMPLE

For n = -11, -10, ..., 22 the primes of the form n^2+3n+9 are 97, 79, 37, 19, 13, 7, 7, 13, 19, 37, 79, 97, 139, 163, 313, 349.

MATHEMATICA

Select[Table[n^2 + 3*n + 9, {n, -1, 200}], PrimeQ] (* T. D. Noe, Mar 21 2013 *)

PROG

(MAGMA) [a: n in [-1..150] | IsPrime(a) where a is  n^2+3*n+9]; // Vincenzo Librandi, Mar 22 2013

CROSSREFS

Sequence in context: A176229 A110074 A058383 * A040096 A181938 A073648

Adjacent sequences:  A005468 A005469 A005470 * A005472 A005473 A005474

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Feb 20 2000

STATUS

approved

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Last modified September 21 17:15 EDT 2014. Contains 247025 sequences.