A161726 a(n) = n^2 - 917*n + 9479.

9479, 8563, 7649, 6737, 5827, 4919, 4013, 3109, 2207, 1307, 409, -487, -1381, -2273, -3163, -4051, -4937, -5821, -6703, -7583, -8461, -9337, -10211, -11083, -11953, -12821, -13687, -14551, -15413, -16273, -17131, -17987, -18841, -19693, -20543, -21391, -22237

Offset: 0

Author

Arkadiusz Wesolowski, Jun 17 2009

Keywords

• easy
• sign

Comments

A prime-generating polynomial of the form f(x) = x^2 - b*x + c.

|a(n)| are distinct primes for 0 <= n <= 29.

The values of this polynomial are never divisible by a prime less than 37. - Arkadiusz Wesolowski, Oct 11 2011

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A005846, A007635, A048059.

Programs

Magma

[n^2-917*n+9479 : n in [0..36]]; // Arkadiusz Wesolowski, Mar 04 2011

Maple

seq(n^2-917*n+9479, n=0..36); # Arkadiusz Wesolowski, Mar 08 2011

Mathematica

Table[n^2 - 917*n + 9479, {n, 0, 36}] (* Arkadiusz Wesolowski, Mar 04 2011 *)

PARI

for(n=0, 36, print1(n^2-917*n+9479, ", ")); \\ Arkadiusz Wesolowski, Mar 02 2011

Formula

G.f.: (-9479 + 19874*x - 10397*x^2)/(x-1)^3. - R. J. Mathar, Mar 08 2011

From Elmo R. Oliveira, Feb 09 2025: (Start)

E.g.f.: exp(x)*(9479 - 916*x + x^2).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

Extensions

Definition and offset changed by R. J. Mathar, Jun 18 2009