

A182255


81n^2  2247n + 15383.


0



15383, 13217, 11213, 9371, 7691, 6173, 4817, 3623, 2591, 1721, 1013, 467, 83, 139, 199, 97, 167, 593, 1181, 1931, 2843, 3917, 5153, 6551, 8111, 9833, 11717, 13763, 15971, 18341, 20873, 23567, 26423, 29441, 32621, 35963, 39467, 43133, 46961, 50951, 55103
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OFFSET

0,1


COMMENTS

The polynomial generates 33 primes/negative values of primes in a row starting from n=0.
The polynomial 81*n^2  2937*n + 26423 generates the same primes in reverse order.
Note: we found in the same family of primegenerating polynomials (with the discriminant equal to 64917 = 3^2*7213) the polynomial 27n^2  753n + 4649 (with its "reversed polynomial" 27n^2  921n + 7253), generating 32 primes in a row and the polynomial 27n^2  741n + 4483 (27n^2  1095n + 10501), generating 35 primes in a row, if we consider that 1 is prime (which seems to be constructive in the study of primegenerating polynomials, at least).
Note: the polynomial 36n^2  810n + 2753, which is the known quadratic polynomial that generates the most distinct primes in a row (45), has the discriminant equal to 259668 = 2^2*3^2*7213.


LINKS

Table of n, a(n) for n=0..40.
E. W. Weisstein, MathWorld: PrimeGenerating Polynomial
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


MATHEMATICA

Table[81n^22247n+15383, {n, 0, 40}] (* or *) LinearRecurrence[{3, 3, 1}, {15383, 13217, 11213}, 50] (* Harvey P. Dale, Jan 17 2019 *)


PROG

(PARI) a(n)=81*n^22247*n+15383 \\ Charles R Greathouse IV, Oct 01 2012


CROSSREFS

Sequence in context: A054834 A232893 A054835 * A054836 A054837 A252990
Adjacent sequences: A182252 A182253 A182254 * A182256 A182257 A182258


KEYWORD

sign,easy


AUTHOR

Marius Coman, Apr 21 2012


STATUS

approved



