%I #31 Feb 16 2025 08:32:47

%S 1753,8779,26209,59197,112921,192583,303409,450649,639577,875491,

%T 1163713,1509589,1918489,2395807,2946961,3577393,4292569,5097979,

%U 5999137,7001581,8110873,9332599,10672369,12135817,13728601,15456403,17324929,19339909,21507097,23832271,26321233,28979809,31813849,34829227

%N a(n) = n^4 + 853n^3 + 2636n^2 + 3536n + 1753.

%C A prime-generating quartic polynomial.

%C For n=0 ... 20, the terms in this sequence are primes. This is not the case for n=21. See A272325 and A272326. - _Robert Price_, Apr 25 2016

%H Harvey P. Dale, <a href="/A076809/b076809.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomials</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: -(x^4-1588*x^3-156*x^2+14*x+1753)/(x- 1)^5. [_Colin Barker_, Nov 11 2012]

%F E.g.f.: (1753 + 7026*x + 5202*x^2 + 859*x^3 + x^4)*exp(x). - _Ilya Gutkovskiy_, Apr 25 2016

%p A076809:=n->n^4 + 853*n^3 + 2636*n^2 + 3536*n + 1753; seq(A076809(n), n=0..100); # _Wesley Ivan Hurt_, Nov 13 2013

%t Table[n^4 + 853n^3 + 2636n^2 + 3536n + 1753, {n,0,100}] (* _Wesley Ivan Hurt_, Nov 13 2013 *)

%t CoefficientList[Series[-(x^4 - 1588 x^3 - 156 x^2 + 14 x + 1753)/(x - 1)^5, {x, 0, 33}], x] (* _Michael De Vlieger_, Apr 25 2016 *)

%t LinearRecurrence[{5,-10,10,-5,1},{1753,8779,26209,59197,112921},40] (* _Harvey P. Dale_, Jan 20 2025 *)

%o (Maxima) A076809(n):=n^4 + 853*n^3 + 2636*n^2 + 3536*n + 1753$

%o makelist(A076809(n),n,0,30); /* _Martin Ettl_, Nov 08 2012 */

%Y Cf. A076808, A272325, A272326.

%K easy,nonn

%O 0,1

%A Hilko Koning (hilko(AT)hilko.net), Nov 18 2002

%E More terms from _Michael De Vlieger_, Apr 25 2016