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.

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

A143835 a(n) = Number of x <= 10^n such that 2x^2-1 is prime.

Original entry on oeis.org

7, 45, 303, 2202, 17185, 141444, 1200975, 10448345, 92435171, 828797351, 7511268020, 68680339342
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008, Sep 04 2008

Keywords

Examples

			a(1) = 7 because are 7 different x ={2, 3, 4, 6, 7, 8, 10} <= 10^1 where 2x^2-1 is prime = {7, 17, 31, 71, 97, 127, 199}.
		

Crossrefs

Programs

  • Mathematica
    l = 0; p = 2; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], l = l + 1]; If[N[Log[x]/Log[10]] == Round[N[Log[x]/Log[10]]], Print[l]; AppendTo[a, l]], {x, 1, 10000000}]; a (*Artur Jasinski*)

Extensions

Added link and extended to agree with website. - Ray Chandler, Jun 30 2015

A143831 Numbers n such that 12n^2 - 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 11, 13, 14, 15, 17, 20, 22, 24, 25, 26, 27, 29, 30, 35, 36, 37, 38, 39, 46, 48, 55, 59, 61, 68, 69, 72, 75, 77, 79, 82, 88, 91, 93, 94, 102, 105, 107, 108, 115, 116, 117, 118, 121, 124, 130, 134, 136, 137, 140, 149, 152, 154, 157, 158, 159, 162, 167
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Crossrefs

Programs

  • Mathematica
    p = 12; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, x]], {x, 1, 1000}]; a
  • PARI
    is(n)=isprime(12*n^2-1) \\ Charles R Greathouse IV, Feb 20 2017

A143833 Numbers n such that 14n^2 - 1 is prime.

Original entry on oeis.org

1, 4, 5, 6, 10, 11, 16, 21, 26, 34, 36, 44, 45, 49, 54, 55, 59, 65, 69, 71, 76, 80, 85, 91, 95, 96, 100, 104, 106, 110, 114, 115, 120, 121, 125, 135, 139, 166, 169, 176, 180, 190, 195, 201, 204, 206, 214, 226, 230, 231, 234, 241, 254, 256, 264, 265, 269, 270, 275, 280
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Crossrefs

Programs

  • Mathematica
    p = 14; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, x]], {x, 1, 1000}]; a
    Select[Range[300],PrimeQ[14#^2-1]&] (* Harvey P. Dale, Aug 29 2011 *)
  • PARI
    is(n)=isprime(14*n^2-1) \\ Charles R Greathouse IV, Feb 20 2017

A143832 Primes of the form 14 n^2-1.

Original entry on oeis.org

13, 223, 349, 503, 1399, 1693, 3583, 6173, 9463, 16183, 18143, 27103, 28349, 33613, 40823, 42349, 48733, 59149, 66653, 70573, 80863, 89599, 101149, 115933, 126349, 129023, 139999, 151423, 157303, 169399, 181943, 185149, 201599, 204973, 218749
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Comments

Primes of the form k n^2-1 k = 2 A066436 these n are A066049 k = 4 only one prime 3 when n = 1 k = 6 A090686 these n are A143826 k = 8 A090684 these n are A143827 k =10 A143828 these n are A143829 k =12 A143830 these n are A143831 k =14 A143832 these n are A143833 k =16 lack of primes

Crossrefs

Programs

  • Mathematica
    p = 14; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, k]], {x, 1, 1000}]; a
    Select[14*Range[200]^2-1,PrimeQ] (* Harvey P. Dale, Jul 29 2024 *)

A143834 Numbers k such that 2k^2 - 1 is not prime.

Original entry on oeis.org

1, 5, 9, 12, 14, 16, 19, 20, 23, 26, 27, 29, 30, 31, 32, 33, 35, 37, 40, 44, 47, 48, 51, 53, 54, 55, 57, 58, 60, 61, 65, 66, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 82, 83, 84, 86, 88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 110, 111, 114, 116, 117
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Comments

Complement of A066049.

Crossrefs

Programs

  • Magma
    [n: n in [1..120]| not IsPrime(2*n^2-1)] // Vincenzo Librandi, Jan 28 2011
  • Mathematica
    p = 2; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k],NULL, AppendTo[a, x]], {x, 1, 1000}]; a
    Select[Range[120],!PrimeQ[2#^2-1]&] (* Harvey P. Dale, Mar 14 2018 *)
Showing 1-6 of 6 results.