A272323 -id:A272323 - cp's OEIS frontend

A076808 a(n) = 82n^3 - 1228n^2 + 6130n - 5861.

-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, 1619803, 1805971

Offset: 0

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

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

Eric Weisstein's World of Mathematics, Prime-Generating Polynomials
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A050266, A076809, A272323, A272324.

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 *)
LinearRecurrence[{4,-6,4,-1},{-5861,-877,2143,3691},40] (* Harvey P. Dale, Jun 18 2018 *)

A076808(n):=82*n^3-1228*n^2+6130*n-5861$
makelist(A076808(n),n,0,30); /* Martin Ettl, Nov 08 2012 */

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

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

A267252 Primes of the form abs(103n^2 - 4707n + 50383) in order of increasing nonnegative n.

Original entry on oeis.org

50383, 45779, 41381, 37189, 33203, 29423, 25849, 22481, 19319, 16363, 13613, 11069, 8731, 6599, 4673, 2953, 1439, 131, 971, 1867, 2557, 3041, 3319, 3391, 3257, 2917, 2371, 1619, 661, 503, 1873, 3449, 5231, 7219, 9413, 11813, 14419, 17231, 20249, 23473, 26903

Offset: 1

Robert Price, Apr 28 2016

This polynomial is a transformed version of the polynomial P(x) = 103*x^2 + 31*x - 3391 whose absolute value gives 43 distinct primes for -23 <= x <= 19, found by G. W. Fung in 1988. - Hugo Pfoertner, Dec 13 2019

			33203 is in this sequence since 103*4^2 - 4707*4 + 50383  = 1648-18828+50383 = 33203 is prime.

Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.

Robert Price, Table of n, a(n) for n = 1..3885
François Dress and Michel Olivier, Polynômes prenant des valeurs premières, Experimental Mathematics, Volume 8, Issue 4 (1999), 319-338.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323, A267069, A330363.

n = Range[0, 100]; Abs @ Select[103n^2 - 4707n + 50383 , PrimeQ[#] &]

lista(nn) = for(n=0, nn, if(isprime(p=abs(103*n^2-4707*n+50383)), print1(p, ", "))); \\ Altug Alkan, Apr 28 2016, corrected by Hugo Pfoertner, Dec 13 2019

Title corrected by Hugo Pfoertner, Dec 13 2019

A272324 Primes of the form abs(82n^3 - 1228n^2 + 6130n - 5861) in order of increasing nonnegative n.

Original entry on oeis.org

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, 2005919, 2693363, 3229579

Offset: 1

Robert Price, Apr 25 2016

nonn

			4259 is in this sequence since 82*4^3 - 1228*4^2 + 6130*4 - 5861 = 5248-19648+24520-5861 = 4259 is prime.

Robert Price, Table of n, a(n) for n = 1..2659
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A076808, A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323.

n = Range[0, 100]; Select[82n^3 - 1228n^2 + 6130n - 5861, PrimeQ[#] &]

A272326 Primes of the form k^4 + 853k^3 + 2636k^2 + 3536*k + 1753 in order of increasing nonnegative k.

Original entry on oeis.org

1753, 8779, 26209, 59197, 112921, 192583, 303409, 450649, 639577, 875491, 1163713, 1509589, 1918489, 2395807, 2946961, 3577393, 4292569, 5097979, 5999137, 7001581, 8110873, 10672369, 15456403, 17324929, 19339909, 26321233, 38031841, 48822439, 66193219

Offset: 1

Robert Price, Apr 25 2016

nonn

			112921 is in this sequence since 4^4 + 853*4^3 + 2636*4^2 + 3536*4 + 1753 = 256+54592+42176+14144+1753 = 112921 is prime.

Robert Price, Table of n, a(n) for n = 1..2457
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323, A272325, A076809.

n = Range[0, 100]; Select[n^4 + 853n^3 + 2636n^2 + 3536n + 1753, PrimeQ[#] &]

lista(nn) = for(n=0, nn, if(isprime(p=n^4+853*n^3+2636*n^2+3536*n+1753), print1(p, ", "))); \\ Altug Alkan, Apr 25 2016

cp's OEIS Frontend

A076808 a(n) = 82n^3 - 1228n^2 + 6130n - 5861.

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A267252 Primes of the form abs(103*n^2 - 4707*n + 50383) in order of increasing nonnegative n.

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A272324 Primes of the form abs(82n^3 - 1228n^2 + 6130n - 5861) in order of increasing nonnegative n.

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A272326 Primes of the form k^4 + 853*k^3 + 2636*k^2 + 3536*k + 1753 in order of increasing nonnegative k.

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A267252 Primes of the form abs(103n^2 - 4707n + 50383) in order of increasing nonnegative n.

A272326 Primes of the form k^4 + 853k^3 + 2636k^2 + 3536*k + 1753 in order of increasing nonnegative k.