OFFSET
0,1
COMMENTS
The polynomial generates 24 primes in absolute value (23 distinct ones) in row starting from n=0 (and 42 primes in absolute value for n from 0 to 46).
The polynomial n^2 - 49*n + 431 generates the same primes in reverse order.
Note: we found in the same family of prime-generating polynomials (with the discriminant equal to 677) the polynomial 13*n^2 - 311*n + 1847 (13*n^2 - 469*n + 4217) generating 23 primes and two noncomposite numbers (in absolute value) in row starting from n=0 (1847, 1549, 1277, 1031, 811, 617, 449, 307, 191, 101, 37, -1, -13, 1, 41, 107, 199, 317, 461, 631, 827, 1049, 1297, 1571, 1871).
Note: another interesting algorithm to produce prime-generating polynomials could be N = m*n^2 + (6*m+1)*n + 8*m + 3, where m, 6*m+1 and 8*m+3 are primes. For m=7 then n=t-20 we get N = 7*t^2 - 237*t + 1999, which generates the following primes: 239, 163, 101, 53, 19, -1, -7, 1, 23, 59, 109, 173, 251 (we can see the same pattern: …, -1, -m, 1, …).
LINKS
Bruno Berselli, 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
G.f.: (-167+338*x-169x^2)/(1-x)^3. - Bruno Berselli, May 18 2012
MATHEMATICA
Table[n^2+3n-167, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {-167, -163, -157}, 50] (* Harvey P. Dale, Feb 08 2020 *)
PROG
(Magma) [n^2+3*n-167: n in [0..47]]; // Bruno Berselli, May 18 2012
(PARI) Vec((-167+338*x-169*x^2)/(1-x)^3+O(x^99)) \\ Charles R Greathouse IV, Oct 01 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Marius Coman, May 14 2012
EXTENSIONS
Edited from Bruno Berselli, May 18 2012
STATUS
approved