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A005471
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Primes of form n^2 + 3n + 9, where n can be positive or negative.
(Formerly M4345)
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17
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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
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OFFSET
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1,1
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COMMENTS
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Primes of the form n^2 + n + 7, for some n >= 0. - Daniel Forgues, Jan 26 2020
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
S. Barbero, U. Cerruti, N. Murru, Identities Involving Zeros of Ramanujan and Shanks Cubic Polynomials, J. Integer Seq., Vol. 16 (2013), Article 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.
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FORMULA
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a(n) == 1 (mod 6). - Zak Seidov, Mar 20 2010
a(n+1) = A175282(n)^2 + 3*A175282(n) + 9. - R. J. Mathar, Jun 06 2019
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EXAMPLE
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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.
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MAPLE
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A005471 := proc(n)
if n = 1 then
7;
else
A175282(n-1)*(3+A175282(n-1))+9 ;
end if;
end proc: # R. J. Mathar, Jun 06 2019
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MATHEMATICA
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Select[Table[n^2 + 3*n + 9, {n, -1, 200}], PrimeQ] (* T. D. Noe, Mar 21 2013 *)
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PROG
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(MAGMA) [a: n in [-1..150] | IsPrime(a) where a is n^2+3*n+9]; // Vincenzo Librandi, Mar 22 2013
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CROSSREFS
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Primes in A027692.
Sequence in context: A266268 A110074 A058383 * A249381 A040096 A181938
Adjacent sequences: A005468 A005469 A005470 * A005472 A005473 A005474
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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