cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

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, 1619803, 1805971
Offset: 0

Views

Author

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

Keywords

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

Crossrefs

Cf. A050266, A076809, A272323, A272324.

Programs

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

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

A095946 Primes of the form 8n^4 - 2n^3 - 132n^2 + 318n + 80557.

Original entry on oeis.org

80557, 80749, 80777, 80917, 81637, 83597, 87649, 94837, 106397, 123757, 148537, 182549, 227797, 286477, 360977, 453877, 567949, 706157, 871657, 1067797, 1298117, 1566349, 1876417, 2232437, 2638717, 3099757, 3620249, 4205077, 4859317
Offset: 1

Views

Author

Hilko Koning (hilko(AT)hilko.net), Jul 13 2004

Keywords

Comments

The first composite has n = 29.

Links

Crossrefs

Cf. A076808, A076809.

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is 8*n^4-2*n^3-132*n^2+ 318*n+80557]; // Vincenzo Librandi, Jul 17 2012
  • Mathematica
    Select[Table[8n^4-2n^3-132n^2+318n+80557,{n,0,2000}],PrimeQ] (* Vincenzo Librandi, Jul 17 2012 *)

A272325 Nonnegative numbers n such that n^4 + 853n^3 + 2636n^2 + 3536n + 1753 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 25, 26, 27, 30, 34, 37, 41, 43, 46, 50, 52, 53, 56, 59, 60, 61, 64, 66, 67, 68, 71, 76, 79, 81, 84, 87, 88, 89, 91, 92, 95, 96, 98, 99, 103, 106, 109, 118, 124, 126, 127, 128, 132
Offset: 1

Views

Author

Robert Price, Apr 25 2016

Keywords

Comments

21 is the smallest number not in this sequence.

Examples

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

Links

Crossrefs

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.
Cf. A271980, A272030, A272074, A272075, A272160, A271144, A272285, A272326, A076809.

Programs

  • Mathematica
    Select[Range[0, 100], PrimeQ[#^4 + 853#^3 + 2636#^2 + 3536# + 1753] &]
  • PARI
    lista(nn) = for(n=0, nn, if(isprime(n^4+853*n^3+2636*n^2+3536*n+1753), print1(n, ", "))); \\ Altug Alkan, Apr 25 2016

A272326 Primes of the form k^4 + 853*k^3 + 2636*k^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

Views

Author

Robert Price, Apr 25 2016

Keywords

Examples

			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.

Links

Crossrefs

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.
Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323, A272325, A076809.

Programs

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

A095974 Evaluate n^4 - 93n^3 + 3196n^2 - 48008n + 265483 for n >= 0, record the primes.

Original entry on oeis.org

265483, 220579, 181523, 147793, 118891, 94343, 73699, 56533, 42443, 31051, 22003, 14969, 9643, 5743, 3011, 1213, 139, -397, -557, -479, -277, -41, 163, 293, 331, 283, 179, 73, 43, 191, 643, 1549, 3083, 5443
Offset: 0

Views

Author

Hilko Koning (hilko(AT)hilko.net), Jul 16 2004

Keywords

Comments

A prime-generating quartic polynomial.

Links

Crossrefs

Cf. A076808, A076809, A095946.

A096372 List of primes produced by a certain "prime-generating" quartic polynomial.

Original entry on oeis.org

1688311, 1410743, 1168619, 958807, 778319, 624311, 494083, 385079, 294887, 221239, 162011, 115223, 79039, 51767, 31859, 17911, 8663, 2999, -53, -1321, -1489, -1097, -541, -73, 199, 311, 443, 919, 2207, 4919, 9811, 17783, 29879, 47287, 71339, 103511, 145423, 198839
Offset: 1

Views

Author

Hilko Koning (hilko(AT)hilko.net), Jul 19 2004

Keywords

Links

Crossrefs

Cf. A076808, A076809, A095946, A095974.

Programs

  • Maple
    f:= n -> 6*n^4 - 558*n^3 + 19354*n^2 - 296370*n + 1688311:
select(isprime@abs, [seq(f(n),n=0..100)]); # Robert Israel, Jan 16 2018
  • Mathematica
    Select[Table[6n^4-558n^3+19354n^2-296370n+1688311,{n,0,40}],PrimeQ] (* Harvey P. Dale, Dec 31 2018 *)

Formula

Evaluate 6n^4 - 558n^3 + 19354n^2 - 296370n + 1688311 for n >= 0, record the primes.

Extensions

Offset changed to 1 by Robert Israel, Jan 16 2018
Showing 1-6 of 6 results.

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