A210527 a(n) = 9*n^2 + 39*n + 83.

83, 131, 197, 281, 383, 503, 641, 797, 971, 1163, 1373, 1601, 1847, 2111, 2393, 2693, 3011, 3347, 3701, 4073, 4463, 4871, 5297, 5741, 6203, 6683, 7181, 7697, 8231, 8783, 9353, 9941, 10547, 11171, 11813, 12473, 13151, 13847, 14561, 15293, 16043, 16811, 17597

Offset

0,1

Comments

This polynomial generates 25 sequential primes numbers for 0 <= n <= 24.

The total number of primes does not go below one-half of the total number of terms generated until n = 862. - Harvey P. Dale, Mar 18 2016

Conjecture: the total number of primes remains below one-half of the total number of terms generated from and after n = 886. - Harvey P. Dale, Mar 18 2016

Links

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Elmo R. Oliveira, Oct 28 2024: (Start)

G.f.: (83 - 118*x + 53*x^2)/(1 - x)^3.

E.g.f.: (83 + 48*x + 9*x^2)*exp(x).

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

Example

a(0)=83, a(1)=131, a(2)=197, a(3)=281, ..., a(24)=6203.

Mathematica

Table[9n^2+39n+83, {n, 0, 200}] (* Harvey P. Dale, Mar 18 2016 *)

Prog

(Maxima) makelist(9*n^2 + 39*n + 83, n, 0, 66); /* Martin Ettl, Feb 12 2013 */
(PARI) a(n)=9*n^2+39*n+83 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A142309 A186465 A142409 * A140038 A260495 A165502

Adjacent sequences: A210524 A210525 A210526 * A210528 A210529 A210530

Keyword

nonn,easy

Author

Tony Herrys Silva Rabelo, Jan 27 2013

Status

approved