A076809 a(n) = n^4 + 853n^3 + 2636n^2 + 3536n + 1753.

1753, 8779, 26209, 59197, 112921, 192583, 303409, 450649, 639577, 875491, 1163713, 1509589, 1918489, 2395807, 2946961, 3577393, 4292569, 5097979, 5999137, 7001581, 8110873, 9332599, 10672369, 12135817, 13728601, 15456403, 17324929, 19339909, 21507097, 23832271, 26321233, 28979809, 31813849, 34829227

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

A prime-generating quartic polynomial.

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomials
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A076808, A272325, A272326.

Programs

Maple

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

Mathematica

Table[n^4 + 853n^3 + 2636n^2 + 3536n + 1753, {n,0,100}] (* Wesley Ivan Hurt, Nov 13 2013 *)
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 *)
LinearRecurrence[{5,-10,10,-5,1},{1753,8779,26209,59197,112921},40] (* Harvey P. Dale, Jan 20 2025 *)

Maxima

A076809(n):=n^4 + 853*n^3 + 2636*n^2 + 3536*n + 1753$
makelist(A076809(n),n,0,30); /* Martin Ettl, Nov 08 2012 */

Formula

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

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

Extensions

More terms from Michael De Vlieger, Apr 25 2016