A143827 -id:A143827 - cp's OEIS frontend

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

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

Artur Jasinski, Sep 02 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

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

[a: n in [1..400] | IsPrime(a) where a is 10*n^2-1]; // Vincenzo Librandi, Dec 07 2011

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

Artur Jasinski, Sep 02 2008

nonn

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

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 *)

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

Artur Jasinski, Sep 02 2008

nonn

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]

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

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

Artur Jasinski, Sep 02 2008, Sep 04 2008

nonn

			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}.

Bernhard Helmes, Prime sieving on the polynomial f(n)=2n^2-1.

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

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*)

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

Artur Jasinski, Sep 02 2008

nonn

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

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

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

Artur Jasinski, Sep 02 2008

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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 *)

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

Artur Jasinski, Sep 02 2008

nonn

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

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

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

Artur Jasinski, Sep 02 2008

nonn

Complement of A066049.

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

[n: n in [1..120]| not IsPrime(2*n^2-1)] // Vincenzo Librandi, Jan 28 2011

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 *)

cp's OEIS Frontend

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

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

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

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

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

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

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

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

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