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 1-10 of 10 results.

A143827 Numbers k such that 8*k^2 - 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 9, 11, 12, 14, 17, 18, 19, 21, 23, 25, 26, 28, 31, 32, 38, 40, 46, 49, 51, 54, 56, 59, 63, 66, 67, 70, 77, 79, 80, 82, 86, 89, 93, 94, 96, 98, 100, 102, 103, 107, 110, 114, 116, 119, 121, 124, 128, 133, 135, 137, 140, 144, 147, 150, 152, 156, 161, 166
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Comments

Contains the even terms of A066049 divided by 2. - R. J. Mathar, Sep 04 2008

Crossrefs

Cf. A090686, A090684.

Programs

  • Mathematica
    p = 8; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, x]], {x, 1, 1000}]; a
  • PARI
    is(n)=isprime(8*n^2-1) \\ Charles R Greathouse IV, Feb 17 2017

A143828 Primes of the form 10*k^2 - 1.

Original entry on oeis.org

89, 359, 809, 1439, 4409, 8999, 10889, 12959, 20249, 23039, 35999, 47609, 51839, 56249, 65609, 75689, 98009, 116639, 123209, 129959, 136889, 143999, 151289, 158759, 166409, 234089, 272249, 282239, 302759, 313289, 334889, 404009, 416159
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Links

Crossrefs

Cf. A066436, A066049, A090686, A090684, A143826, A143827.

Programs

  • Magma
    [a: n in [1..400] | IsPrime(a) where a is 10*n^2-1]; // Vincenzo Librandi, Dec 07 2011
  • Mathematica
    p = 10; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, k]], {x, 1, 1000}]; a
Select[Table[10n^2-1,{n,1,800}],PrimeQ] (* Vincenzo Librandi, Dec 07 2011 *)

A143829 Numbers n such that 10n^2 - 1 is prime.

Original entry on oeis.org

3, 6, 9, 12, 21, 30, 33, 36, 45, 48, 60, 69, 72, 75, 81, 87, 99, 108, 111, 114, 117, 120, 123, 126, 129, 153, 165, 168, 174, 177, 183, 201, 204, 207, 222, 234, 243, 252, 267, 279, 282, 285, 294, 303, 312, 315, 318, 339, 345, 348, 369, 378, 381, 384, 393, 396
Offset: 1

Views

Author

Artur Jasinski, Sep 02 2008

Keywords

Crossrefs

A066436, A066049, A090686, A090684, A143826, A143827, A143828

Programs

  • Mathematica
    p = 10; a = {}; Do[k = p x^2 - 1; If[PrimeQ[k], AppendTo[a, x]], {x, 1, 1000}]; a
Select[Range[500],PrimeQ[10#^2-1]&] (* Harvey P. Dale, Nov 11 2020 *)
  • PARI
    is(n)=isprime(10*n^2-1) \\ Charles R Greathouse IV, Feb 17 2017

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

A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829

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}.

Links

Crossrefs

Cf. A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143832, A143833, A143834.

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

Cf. A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830.

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

Links

Crossrefs

Cf. A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143832.

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

A188382 Primes of the form 8*n^2 + 2*n + 1.

Original entry on oeis.org

11, 37, 79, 137, 211, 821, 991, 1597, 1831, 2081, 2347, 2927, 3571, 3917, 4657, 5051, 6329, 8779, 9871, 11027, 14197, 14879, 17021, 20101, 21737, 26107, 27967, 28921, 33931, 34981, 39341, 40471, 41617, 50087, 51361, 59341
Offset: 1

Views

Author

Alonso del Arte, Mar 29 2011

Keywords

Comments

In a variant of the Ulam spiral with only odd numbers, prime numbers can line up in horizontal or vertical lines rather than diagonal lines. These primes are on one such horizontal (or vertical) line.
Primes in A188135. Primes in the sequence found by reading the line from 1, in the direction 1, 11, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011
Equivalently, primes of the form 2*n^2+n+1. - N. J. A. Sloane, Nov 08 2014

Links

Crossrefs

Cf. A090684, A187677.

Programs

  • Magma
    [ a: n in [0..250] | IsPrime(a) where a is 8*n^2 + 2*n + 1 ]; // Vincenzo Librandi, Apr 05 2011
  • Maple
    select(isprime,[seq(8*n^2+2*n+1,n=0..86)]); # Peter Luschny, Aug 22 2011
  • Mathematica
    Select[Table[8n^2 + 2n + 1, {n, 100}], PrimeQ]
  • PARI
    select(isprime, vector(1000,n,8*n^2+2*n+1)) \\ Charles R Greathouse IV, Jun 14 2011

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

A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143833

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

Cf. A066436, A066049, A090686, A090684, A143826, A143827, A143828, A143829, A143830, A143831, A143833.

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 1-10 of 10 results.

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

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