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 1-5 of 5 results.

A162291 Primes of the form n^3-n^2-1.

Original entry on oeis.org

3, 17, 47, 179, 293, 647, 1583, 2027, 5507, 8819, 10163, 26099, 34847, 95219, 108287, 181943, 191747, 223259, 283139, 296273, 416249, 486797, 606899, 650933, 720899, 821747, 875519, 960497, 989999, 1179779, 1355309, 1468547, 1587923, 1629107
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

Comments

Generated by the n of A162293.

Links

Crossrefs

Cf. A087908, A162293 (corresponding n).

Programs

  • Mathematica
    Select[Table[n^3-n^2-1,{n,0,250}],PrimeQ] (* Harvey P. Dale, Dec 08 2013 *)

Formula

A087908 INTERSECT A000040 - R. J. Mathar, Jul 31 2007

Extensions

Comment abbreviated by R. J. Mathar, Jul 31 2007

A162293 Numbers k such that k^2*(k-1)-1 is prime.

Original entry on oeis.org

2, 3, 4, 6, 7, 9, 12, 13, 18, 21, 22, 30, 33, 46, 48, 57, 58, 61, 66, 67, 75, 79, 85, 87, 90, 94, 96, 99, 100, 106, 111, 114, 117, 118, 120, 121, 127, 129, 133, 138, 144, 153, 160, 162, 171, 174, 175, 186, 187, 195, 199, 202, 204, 220, 222, 223, 231, 243, 246, 252
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

Examples

			a(1)=2 since 2^3-2^2-1=3 is prime.
a(2)=3 since 3^3-3^2-1=17 is prime.
a(3)=4 since 4^3-4^2-1=47 is prime.

Links

Crossrefs

Cf. A087908, A162291 (corresponding primes), A111501.

Programs

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

Formula

a(n)^2 * ( a(n)-1 )-1 = A162291(n).

Extensions

Comments moved to the examples by R. J. Mathar, Sep 11 2009

A162294 Numbers k such that k^3-k^2-k-1 is prime.

Original entry on oeis.org

4, 6, 8, 12, 16, 22, 28, 34, 44, 50, 54, 56, 58, 76, 78, 88, 110, 112, 118, 134, 138, 156, 162, 166, 168, 170, 188, 190, 200, 204, 208, 210, 226, 230, 236, 244, 250, 268, 274, 302, 310, 314, 322, 324, 340, 344, 356, 364, 368, 378, 382, 390, 398, 400, 420, 424
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

Examples

			k=4 is in the sequence because 4^3-4^2-4-1=43 is prime.
k=6 is in the sequence because 6^3-6^2-6-1=173 is prime.

Links

Crossrefs

Cf. A087908, A111501, A162291, A162293, A162295 (corresponding primes).

Programs

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

Formula

k^3-k^2-k-1 = A162295(n), where k=a(n).
Sum_{i=1..n} a(i) = Sum_{i=1..n} i * ( pi(i^3 - i^2 - i - 1) - pi(i^3 - i^2 - i - 2) ). - Wesley Ivan Hurt, May 24 2013

Extensions

Edited by R. J. Mathar, Jul 02 2009

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

A162292 Primes of the form k^3-k^2+1, k>0.

Original entry on oeis.org

5, 19, 101, 181, 449, 2029, 2549, 8821, 13249, 16901, 21169, 23549, 34849, 38149, 41651, 45361, 62401, 77659, 89101, 108289, 115249, 122501, 130051, 163351, 191749, 433201, 505601, 564899, 697049, 720901, 795709, 875521, 960499, 990001
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

Examples

			a(1)=2^3-2^2+1=5. a(2)=3^3-3^2+1=19. a(3)=5^3-5^2+1=101.

Links

Crossrefs

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

Programs

  • Mathematica
    lst={};Do[s=n^3-n^2;If[PrimeQ[s+1],AppendTo[lst,s+1]],{n,4*5!}];lst

Formula

a(n)= A111501(n)^3-A111501(n)^2+1 .

Extensions

Edited by R. J. Mathar, Jul 02 2009
Showing 1-5 of 5 results.

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