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A076808 a(n) = 82n^3 - 1228n^2 + 6130n - 5861. 10
-5861, -877, 2143, 3691, 4259, 4339, 4423, 5003, 6571, 9619, 14639, 22123, 32563, 46451, 64279, 86539, 113723, 146323, 184831, 229739, 281539, 340723, 407783, 483211, 567499, 661139, 764623, 878443, 1003091, 1139059, 1286839, 1446923 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A prime-generating cubic polynomial.

For n=0 ... 31, the absolute value of terms in this sequence are primes.  This is not the case for n=32. See A272323 and A272324. - Robert Price, Apr 25 2016

LINKS

Table of n, a(n) for n=0..31.

Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: (13301*x^3-29515*x^2+22567*x-5861)/(x-1)^4. - Colin Barker, Nov 10 2012

E.g.f.: (-5861 + 4984*x - 982*x^2 + 82*x^3)*exp(x). - Ilya Gutkovskiy, Apr 25 2016

MATHEMATICA

Table[82 n^3 - 1228 n^2 + 6130 n - 5861, {n, 0, 31}] (* or *)

CoefficientList[Series[(13301 x^3 - 29515 x^2 + 22567 x - 5861)/(x - 1)^4, {x, 0, 31}], x] (* Michael De Vlieger, Apr 25 2016 *)

PROG

(Maxima) A076808(n):=82*n^3-1228*n^2+6130*n-5861$

makelist(A076808(n), n, 0, 30); /* Martin Ettl, Nov 08 2012 */

(PARI) a(n)=82*n^3-1228*n^2+6130*n-5861 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A050266, A076809, A272323, A272324.

Sequence in context: A031830 A219008 A020416 * A272324 A104927 A183843

Adjacent sequences:  A076805 A076806 A076807 * A076809 A076810 A076811

KEYWORD

easy,sign

AUTHOR

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

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.