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 1-3 of 3 results.

A162295 Primes of the form k^3-k^2-k-1.

Original entry on oeis.org

43, 173, 439, 1571, 3823, 10141, 21139, 38113, 83203, 122449, 154493, 172423, 191689, 433123, 468389, 673639, 1318789, 1392271, 1628989, 2388013, 2608889, 3771923, 4225121, 4546573, 4713239, 4883929, 6609139, 6822709, 7959799
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

Examples

			a(1)=4^3-4^2-4-1=43. a(2)=6^3-6^2-6-1=173.

Links

Crossrefs

Cf. A087908, A162291, A111501, A162293, A162294, A162294 (corresponding k).

Programs

  • Mathematica
    lst={};Do[p=n^3-n^2-n-1;If[PrimeQ[p],AppendTo[lst,p]],{n,2,6!}];lst

Formula

a(n)=k^3-k^2-k-1 where k=A162294(n).

Extensions

Edited by R. J. Mathar, Jul 02 2009

A173179 Numbers n such that n^4-n^3-n^2-n-1 is prime.

Original entry on oeis.org

3, 8, 9, 11, 14, 17, 18, 20, 24, 27, 38, 41, 45, 48, 50, 51, 56, 59, 60, 62, 63, 71, 77, 78, 81, 84, 86, 87, 90, 92, 93, 95, 101, 111, 113, 114, 119, 146, 147, 153, 155, 171, 179, 186, 204, 207, 219, 225, 230, 231, 233, 234, 240, 246, 254, 255, 267, 284, 287, 291
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Comments

All terms == 0 or 2 (mod 3). - Robert Israel, Mar 09 2020

Links

Crossrefs

Cf. A125082, A002328, A162294.

Programs

  • Magma
    [n: n in [2..350] | IsPrime(n^4 - n^3 - n^2 - n - 1)]; // Vincenzo Librandi, Mar 16 2020
  • Maple
    select(t -> isprime(t^4-t^3-t^2-t-1), [$2..1000]); # Robert Israel, Mar 09 2020
  • Mathematica
    f[n_]:=n^4-n^3-n^2-n-1;Select[Range[6! ],PrimeQ[f[ #1]]&]
  • PARI
    is(n)=isprime(n^4-n^3-n^2-n-1) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

Edited by N. J. A. Sloane, Apr 10 2010

A173180 Numbers k such that k^5-k^4-k^3-k^2-k-1 is prime.

Original entry on oeis.org

4, 6, 8, 14, 18, 20, 24, 26, 28, 32, 40, 42, 50, 58, 62, 68, 72, 100, 104, 120, 122, 140, 150, 174, 184, 192, 210, 234, 240, 260, 266, 278, 288, 300, 306, 326, 346, 366, 404, 432, 444, 460, 464, 466, 470, 484, 488, 512, 516, 526, 538, 556, 562, 564, 570, 584
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Comments

All terms are even. - Robert Israel, Apr 11 2019

Links

Crossrefs

Cf. A002328, A008864, A162294, A173179

Programs

  • Maple
    filter:= k -> isprime( k^5-k^4-k^3-k^2-k-1):
select(filter, 2*[$1..500]); # Robert Israel, Apr 11 2019
  • Mathematica
    f[n_]:=n^5-n^4-n^3-n^2-n-1;Select[Range[7! ],PrimeQ[f[ #1]]&]
Select[Range[2,600,2],PrimeQ[#^5-Total[#^Range[0,4]]]&] (* Harvey P. Dale, Sep 26 2023 *)

Formula

{k: A125083(k) in A000040}. [R. J. Mathar, Feb 13 2010]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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