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 prime-generating 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 prime-generating 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
E. W. Weisstein, MathWorld: Prime-Generating Polynomial
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
MATHEMATICA
Table[81n^2-2247n+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^2-2247*n+15383 \\ Charles R Greathouse IV, Oct 01 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Marius Coman, Apr 21 2012
STATUS
approved