OFFSET
0,1
COMMENTS
The polynomial generates 35 primes/negative values of primes in row starting from n=0.
The polynomial 4*n^2 - 284*n + 3449 generates the same primes in reverse order.
Other related polynomials:
For n = 6n+6 than n = n-11 we get 144n^2 - 2808n + 12097 which generates 16 primes in row starting from n=0 (with the discriminant equal to 2^9*3^2*199);
For n = 12n+12 than n = n-15 we get 576n^2 - 15984n + 109297 which generates 17 primes in row starting from n=0 (with the discriminant equal to 2^11*3^2*199).
So this polynomial opens at least two directions of study:
(1) polynomials of type 4n^2 + 12n - p, where p is prime (could be of the form 30k+23);
(2) polynomials with the discriminant equal to 2^n*3^m*199, where n is odd and m is even (an example of such a polynomial, with the discriminant equal to 2^5*3^4*199, is 36n^2 - 1020n + 3643 which generates 32 primes for values of n from 0 to 34).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
E. W. Weisstein, MathWorld: Prime-Generating Polynomial
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Chai Wah Wu, May 28 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (1591*x^2 - 3182*x + 1583)/(x - 1)^3.
(End)
MATHEMATICA
Table[4 n^2 + 12 n - 1583, {n, 0, 50}] (* Vincenzo Librandi, May 29 2016 *)
PROG
(PARI) a(n)=4*n^2+12*n-1583 \\ Charles R Greathouse IV, Oct 01 2012
(Magma) [4*n^2+12*n-1583: n in [0..50]]; // Vincenzo Librandi, May 29 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Marius Coman, May 09 2012
STATUS
approved