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 1-4 of 4 results.

A285790 Primes equal to a hexagonal number plus 1.

Original entry on oeis.org

2, 7, 29, 67, 191, 277, 379, 631, 947, 1129, 1327, 2017, 2557, 2851, 4561, 4951, 5779, 6217, 8647, 9181, 12721, 13367, 14029, 15401, 16111, 17579, 20707, 21529, 22367, 24091, 24977, 31627, 36857, 37951, 42487, 43661, 44851, 47279, 53629, 58997, 64621, 66067
Offset: 1

Views

Author

Colin Barker, Apr 26 2017

Keywords

Comments

Apart from the leading 2 the same as A176616. - R. J. Mathar, Apr 27 2017
Primes in A130883. - Omar E. Pol, Apr 27 2017

Links

Crossrefs

Cf. A000040, A000384, A002496, A055469, A285789, A285791, A176616, A285792.

Programs

  • Mathematica
    Select[PolygonalNumber[6,Range[200]]+1,PrimeQ] (* Harvey P. Dale, Jun 16 2022 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
maxk=300; L=List(); for(k=1, maxk, if(isprime(p=pg(6, k) + 1), listput(L, p))); Vec(L)

A176617 Primes of the form 14*k^2 + 26*k + 13.

Original entry on oeis.org

13, 53, 673, 881, 1117, 1381, 1993, 2341, 3121, 4013, 6133, 6733, 8017, 9413, 11717, 12541, 25801, 27017, 36313, 43793, 51973, 53693, 55441, 59021, 64601, 80713, 85021, 96281, 100981, 123517, 128833, 139801, 160073, 169181, 175393, 181717
Offset: 1

Views

Author

Giovanni Teofilatto, Apr 22 2010

Keywords

Comments

All terms are congruent to 1 (mod 4).

Crossrefs

Cf. A176608, A176616.

Programs

  • Magma
    [ a: n in [0..250] | IsPrime(a) where a is 14*n^2+26*n+13 ] // Vincenzo Librandi, Apr 25 2010
  • Mathematica
    Select[Table[14n^2+26n+13, {n,0,200}], PrimeQ] (* Harvey P. Dale, Jan 04 2011 *)

Extensions

Definition made more precise by R. J. Mathar, May 04 2010
Corrected (inserted 13) and extended by Vincenzo Librandi, Apr 25 2010

A176622 Primes of the form x^2 + 17*y^2, where x and y=x+1 are consecutive natural numbers.

Original entry on oeis.org

17, 157, 281, 4021, 8669, 10321, 14057, 16141, 37997, 58369, 71317, 78277, 80669, 93169, 109357, 112181, 117937, 136069, 176221, 179801, 187069, 198241, 213641, 225569, 237821, 285517, 299281, 318137, 393977, 410117, 443369, 507697, 513761
Offset: 1

Views

Author

Giovanni Teofilatto, Apr 22 2010

Keywords

Comments

a(n) is congruent 1 mod 4.

Links

Crossrefs

Cf. A176608, A176616, A176617.

Programs

  • Magma
    [a: n in [1..250]|IsPrime(a) where a is 18*n^2+34*n+17] // Vincenzo Librandi, Dec 04 2010
  • Mathematica
    Select[Table[18x^2+34x+17,{x,0,200}],PrimeQ] (* Harvey P. Dale, May 06 2017 *)

Extensions

Constraint y=x+1 added to definition by R. J. Mathar, May 04 2010
Extended by Vincenzo Librandi, Apr 25 2010

A176695 Primes of the form x^2 + 29*(x+1)^2.

Original entry on oeis.org

29, 1069, 4297, 7649, 18701, 21817, 34613, 45553, 52837, 60661, 63389, 71933, 77929, 81017, 90641, 107881, 111509, 122753, 155377, 168601, 187073, 201557, 264893, 369409, 376097, 438989, 476029, 498973, 579353, 674701, 711173, 767681
Offset: 1

Views

Author

Giovanni Teofilatto, Apr 24 2010

Keywords

Comments

a(n) == 1 (mod 4).

Links

Crossrefs

Cf. A176608, A176616, A176617.

Programs

  • Magma
    [ a: n in [0..250] | IsPrime(a) where a is 30*n^2+58*n+29 ] // Vincenzo Librandi, Apr 25 2010
  • Mathematica
    Select[Table[x^2 + 29(x + 1)^2, {x, 0, 200}], PrimeQ] (* Harvey P. Dale, Dec 12 2010 *)

Extensions

Corrected and extended by Vincenzo Librandi, Apr 25 2010
Showing 1-4 of 4 results.

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

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