A210527 - OEIS

%I #22 Oct 28 2024 19:40:32

%S 83,131,197,281,383,503,641,797,971,1163,1373,1601,1847,2111,2393,

%T 2693,3011,3347,3701,4073,4463,4871,5297,5741,6203,6683,7181,7697,

%U 8231,8783,9353,9941,10547,11171,11813,12473,13151,13847,14561,15293,16043,16811,17597

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

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

%C 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

%C 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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F From _Elmo R. Oliveira_, Oct 28 2024: (Start)

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

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

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

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

%t Table[9n^2+39n+83,{n,0,200}] (* _Harvey P. Dale_, Mar 18 2016 *)

%o (Maxima) makelist(9*n^2 + 39*n + 83,n,0,66); /* _Martin Ettl_, Feb 12 2013 */

%o (PARI) a(n)=9*n^2+39*n+83 \\ _Charles R Greathouse IV_, Jun 17 2017

%K nonn,easy

%O 0,1

%A _Tony Herrys Silva Rabelo_, Jan 27 2013