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.

A201715 Primes of the form 3*m^2 - 2.

Original entry on oeis.org

73, 241, 673, 1321, 1873, 2521, 3673, 4561, 6073, 11161, 14281, 15121, 19681, 21673, 23761, 24841, 27073, 29401, 33073, 49921, 51481, 54673, 63073, 66601, 72073, 77761, 87721, 91873, 102673, 109441, 114073, 118801, 131041, 143881
Offset: 1

Views

Author

Vincenzo Librandi, Dec 04 2011

Keywords

Comments

Primes p such that 3*(p+2) or (p+2)/3 is a square. - Vincenzo Librandi, Feb 16 2016
m is a member of A063213. - Bruno Berselli, Feb 16 2016

Crossrefs

Programs

  • Magma
    [a: n in [1..300] | IsPrime(a) where a is 3*n^2-2];
  • Mathematica
    Select[Table[3 n^2 - 2, {n, 1, 800}], PrimeQ]

A201716 Primes of the form 3*m^2 - 4.

Original entry on oeis.org

23, 71, 239, 359, 503, 863, 1319, 1583, 1871, 2879, 3671, 5039, 8423, 9743, 11159, 11903, 12671, 13463, 16871, 17783, 18719, 20663, 25943, 29399, 33071, 38303, 39671, 48383, 49919, 51479, 61343, 68399, 70223, 73943, 81671, 83663, 87719
Offset: 1

Views

Author

Vincenzo Librandi, Dec 04 2011

Keywords

Comments

Primes p such that 3*(p+4) or (p+4)/3 is a square. - Vincenzo Librandi, Dec 05 2015, Feb 16 2016

Examples

			23 is in the sequence because 3 * 3^2 - 4 = 27 - 4 = 23.
71 = 3 * 5^2 - 4.
143 is not in the sequence, because 3 * 7^2 - 4 = 143 but 11 * 13 = 143.
		

Crossrefs

Programs

  • Magma
    [a: n in [1..300] | IsPrime(a) where a is 3*n^2-4];
    
  • Maple
    select(isprime, [seq(3*(2*k+1)^2-4, k = 1..1000)]); # Robert Israel, Nov 09 2014
  • Mathematica
    Select[Table[3n^2 - 4, {n, 1000}], PrimeQ]
  • PARI
    lista(nn) = for (k=0, nn, if (isprime(p=3*k^2-4), print1(p, ", "))); \\ Michel Marcus, Nov 19 2014, Feb 16 2016

A201717 Primes of the form 3*m^2 - 5.

Original entry on oeis.org

7, 43, 103, 967, 1447, 1723, 2347, 3067, 3463, 4327, 6343, 6907, 9403, 11527, 13063, 21163, 23227, 28807, 32443, 33703, 44647, 47623, 52267, 65707, 71143, 74887, 80683, 88747, 90823, 99367, 110587, 137383, 142567, 150523, 175687
Offset: 1

Views

Author

Vincenzo Librandi, Dec 05 2011

Keywords

Comments

Primes p such that 3*(p+5) or (p+5)/3 is a square. - Vincenzo Librandi, Feb 16 2016

Crossrefs

Cf. A000040, A042993 (supersequence).
Cf. similar sequences: A089682, A201715, A201716, A201718, A201781.

Programs

  • Magma
    [a: n in [2..300] | IsPrime(a) where a is 3*n^2-5];
  • Mathematica
    Select[Table[3n^2-5,{n,2,1000}],PrimeQ]

A143830 Primes of the form 12*n^2-1.

Original entry on oeis.org

11, 47, 107, 191, 431, 587, 971, 1451, 2027, 2351, 2699, 3467, 4799, 5807, 6911, 7499, 8111, 8747, 10091, 10799, 14699, 15551, 16427, 17327, 18251, 25391, 27647, 36299, 41771, 44651, 55487, 57131, 62207, 67499, 71147, 74891, 80687, 92927, 99371
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Comments

Equals A089682 without the 2. [Sketch of proof: the primes 3*n^2-1 are odd if 2 is left out, so 3*n^2 is even, so n^2 is even, so n is even = 2*k. 3*(2*k)^2-1 = 12*k^2-1.] [From R. J. Mathar, Sep 04 2008]

Crossrefs

Programs

  • Mathematica
    p = 12; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, k]], {x, 1, 1000}]; a

A201718 Primes of the form 3*m^2 - 7.

Original entry on oeis.org

5, 41, 101, 293, 761, 1193, 1721, 2693, 3461, 3881, 4793, 5801, 8741, 12281, 16421, 17321, 26501, 32441, 36293, 40361, 53861, 62201, 67493, 80681, 86693, 90821, 92921, 101561, 108293, 112901, 119993, 127301, 145193, 167081, 178601, 193541
Offset: 1

Views

Author

Vincenzo Librandi, Dec 05 2011

Keywords

Comments

Primes p such that (p+7)/3 or 3*(p+7) is a square. - Vincenzo Librandi, Feb 16 2016

Crossrefs

Programs

  • Magma
    [a: n in [2..300] | IsPrime(a) where a is 3*n^2-7];
  • Mathematica
    Select[Table[3 n^2 - 7, {n, 2, 1000}], PrimeQ]

A201781 Primes of the form 3*m^2 - 8.

Original entry on oeis.org

19, 67, 139, 499, 859, 1579, 1867, 2179, 3259, 4099, 6067, 6619, 8419, 9067, 9739, 22699, 25939, 27067, 28219, 38299, 39667, 46867, 54667, 56299, 61339, 63067, 73939, 79699, 81667, 89779, 91867, 93979, 100459, 102667, 114067, 123619
Offset: 1

Views

Author

Vincenzo Librandi, Dec 05 2011

Keywords

Comments

m is a member of A063241. - Bruno Berselli, Feb 16 2016

Crossrefs

Programs

  • Magma
    [a: n in [2..300] | IsPrime(a) where a is 3*n^2-8];
  • Mathematica
    Select[Table[3n^2 - 8, {n, 2, 1000}], PrimeQ]
Showing 1-6 of 6 results.