A105126 -id:A105126 - cp's OEIS frontend

A105129 Primes of the form 128n+65.

193, 449, 577, 1217, 1601, 2113, 2753, 3137, 4289, 4673, 4801, 5441, 5569, 5953, 6337, 6977, 7489, 7873, 8513, 8641, 9281, 10177, 10433, 11329, 11969, 12097, 13121, 13249, 13633, 14401, 14657, 15809, 15937, 16193, 17729, 19009, 19777, 20161, 20929, 21313

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002145, A007521, A105126-A105132.

[ a: n in [0..200] | IsPrime(a) where a is 128*n+65 ]; // Vincenzo Librandi, Jul 19 2012

Select[128*Range[0,200]+65,PrimeQ] (* Harvey P. Dale, Apr 17 2012 *)
Select[Table[128*n+65,{n,0,700}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

A325069 Prime numbers congruent to 9 modulo 16 representable by x^2 + 32*y^2.

Original entry on oeis.org

41, 137, 313, 409, 457, 521, 569, 761, 809, 857, 953, 1129, 1321, 1657, 1993, 2137, 2153, 2297, 2377, 2521, 2617, 2633, 2713, 2729, 2777, 2953, 3001, 3209, 3433, 3593, 3769, 3881, 3929, 4073, 4441, 4649, 4729, 4793, 4889, 4969, 5273, 5417, 5449, 5641, 5657

Offset: 1

Rémy Sigrist, Mar 27 2019

nonn

Kaplansky showed that prime numbers congruent to 9 modulo 16 are representable by exactly one of the quadratic forms x^2 + 32*y^2 or x^2 + 64*y^2. This sequence corresponds to those representable by the first form and A325070 to those representable by the second form.

			Regarding 41:
- 41 is a prime number,
- 41 = 2*16 + 9,
- 41 = 3^2 + 32*1^2,
- hence 41 belongs to this sequence.

David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.
Rémy Sigrist, PARI program for A325069
Wikipedia, Kaplansky's theorem on quadratic forms

See A325067 for similar results.

Cf. A105126.

PARI
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See Links section.
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A325070 Prime numbers congruent to 9 modulo 16 representable by x^2 + 64*y^2.

Original entry on oeis.org

73, 89, 233, 281, 601, 617, 937, 1033, 1049, 1097, 1193, 1289, 1433, 1481, 1609, 1721, 1753, 1801, 1913, 2089, 2281, 2393, 2441, 2473, 2857, 2969, 3049, 3257, 3449, 3529, 3673, 3833, 4057, 4153, 4201, 4217, 4297, 4409, 4457, 4937, 5081, 5113, 5209, 5689, 5737

Offset: 1

Rémy Sigrist, Mar 27 2019

nonn

Kaplansky showed that prime numbers congruent to 9 modulo 16 are representable by exactly one of the quadratic forms x^2 + 32*y^2 or x^2 + 64*y^2. A325069 corresponds to those representable by the first form and this sequence to those representable by the second form.

			Regarding 4201:
- 4201 is a prime number,
- 4201 = 262*16 + 9,
- 4201 = 51^2 + 64*5^2,
- hence 4201 belongs to this sequence.

David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.
Rémy Sigrist, PARI program for A325070
Wikipedia, Kaplansky's theorem on quadratic forms

See A325067 for similar results.

Cf. A105126, A325069.

PARI
```
See Links section.
```

A105128 Primes of the form 64n+33.

Original entry on oeis.org

97, 353, 673, 929, 1249, 1697, 1889, 2017, 2081, 2273, 2593, 2657, 3041, 3169, 3361, 3617, 4001, 4129, 4513, 5153, 5281, 5857, 6113, 6689, 7393, 7457, 7649, 7841, 8161, 8353, 8609, 8737, 8929, 9377, 9697, 10273, 10337, 10529, 10657, 11489, 11617, 11681

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002145, A007521, A105126-A105132.

[ a: n in [0..200] | IsPrime(a) where a is 64*n+33]; // Vincenzo Librandi, Jul 19 2012

Select[Table[64*n+33,{n,0,700}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

A105130 Primes of the form 256n+129.

Original entry on oeis.org

641, 1153, 1409, 2689, 3457, 4481, 4993, 6529, 7297, 9601, 9857, 10369, 11393, 12161, 13441, 13697, 15233, 16001, 18049, 19073, 19841, 20353, 21121, 21377, 26497, 28289, 29569, 30593, 31873, 33409, 35201, 35969, 38273, 39041, 40577, 43649, 44417, 45697

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002145, A007521, A105126-A105132.

[ a: n in [0..200] | IsPrime(a) where a is 256*n+129 ]; // Vincenzo Librandi, Jul 19 2012

Select[Table[256*n+129,{n,0,700}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

A105134 Numbers n such that 16n+9 is prime.

Original entry on oeis.org

2, 4, 5, 8, 14, 17, 19, 25, 28, 32, 35, 37, 38, 47, 50, 53, 58, 59, 64, 65, 68, 70, 74, 80, 82, 89, 92, 100, 103, 107, 109, 112, 119, 124, 130, 133, 134, 142, 143, 148, 149, 152, 154, 157, 163, 164, 169, 170, 173, 178, 184, 185, 187, 190, 200, 203, 214, 215, 220, 224, 229

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

[n: n in [0..500] | IsPrime(16*n+9)]; // Vincenzo Librandi, Jan 07 2013

Select[Range[0, 500], PrimeQ[16 # + 9]&] (* Vincenzo Librandi, Jan 07 2013 *)

is(n)=isprime(16*n+9) \\ Charles R Greathouse IV, Jun 06 2017

A105138 Numbers n such that 256n+129 is prime.

Original entry on oeis.org

2, 4, 5, 10, 13, 17, 19, 25, 28, 37, 38, 40, 44, 47, 52, 53, 59, 62, 70, 74, 77, 79, 82, 83, 103, 110, 115, 119, 124, 130, 137, 140, 149, 152, 158, 170, 173, 178, 179, 193, 200, 205, 208, 209, 212, 217, 230, 235, 238, 242, 247, 248, 257, 268, 269, 272, 275, 280, 283, 299, 307

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

[n: n in [0..350] | IsPrime(256*n+129)]; // Vincenzo Librandi, Jan 08 2013

Select[Range[0, 500], PrimeQ[256 # + 129]&] (* Vincenzo Librandi, Jan 08 2013 *)

is(n)=isprime(256*n+129) \\ Charles R Greathouse IV, Jun 12 2017

A105139 Numbers k such that 512*k+257 is prime.

Original entry on oeis.org

0, 1, 6, 15, 18, 27, 28, 43, 45, 52, 60, 61, 70, 73, 78, 81, 85, 90, 96, 97, 111, 112, 117, 138, 147, 151, 153, 165, 172, 178, 187, 192, 196, 202, 208, 210, 211, 213, 216, 222, 228, 231, 235, 243, 250, 252, 253, 255, 262, 265, 270, 280, 291, 298, 301, 312, 325, 328, 330, 337

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

[n: n in [0..350] | IsPrime(512*n + 257)]; // Vincenzo Librandi, Jan 08 2013

Select[Range[0, 500], PrimeQ[512 # + 257]&] (* Vincenzo Librandi, Jan 08 2013 *)

is(n)=isprime(512*n+257) \\ Charles R Greathouse IV, Jun 06 2017

A105135 Numbers n such that 32n+17 is prime.

Original entry on oeis.org

0, 3, 7, 10, 12, 13, 18, 27, 30, 31, 37, 40, 42, 46, 48, 55, 58, 66, 67, 75, 81, 87, 88, 90, 96, 97, 100, 103, 115, 117, 118, 121, 126, 130, 132, 133, 135, 142, 145, 147, 150, 156, 163, 165, 168, 172, 195, 198, 201, 202, 205, 208, 210, 213, 217, 220, 222, 235, 243, 250, 252

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

[n: n in [0..500] | IsPrime(32*n+17)]; // Vincenzo Librandi, Jan 07 2013

Select[Range[0, 260], PrimeQ[32 # + 17]&] (* Harvey P. Dale, Apr 26 2011 *)

is(n)=isprime(32*n+17) \\ Charles R Greathouse IV, Jun 12 2017

A105136 Numbers n such that 64n+33 is prime.

Original entry on oeis.org

1, 5, 10, 14, 19, 26, 29, 31, 32, 35, 40, 41, 47, 49, 52, 56, 62, 64, 70, 80, 82, 91, 95, 104, 115, 116, 119, 122, 127, 130, 134, 136, 139, 146, 151, 160, 161, 164, 166, 179, 181, 182, 196, 197, 206, 211, 214, 217, 221, 224, 227, 230, 235, 236, 239, 244, 250, 251, 256, 257

Offset: 1

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

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

Cf. A095278, A105133-A105140, A002145, A007521, A105126-A105132.

Select[Range[300],PrimeQ[64#+33]&] (* Harvey P. Dale, Sep 19 2011 *)

is(n)=isprime(64*n+33) \\ Charles R Greathouse IV, Jun 12 2017

cp's OEIS Frontend

A105129 Primes of the form 128n+65.

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A325069 Prime numbers congruent to 9 modulo 16 representable by x^2 + 32*y^2.

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PARI

A325070 Prime numbers congruent to 9 modulo 16 representable by x^2 + 64*y^2.

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Examples

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Programs

PARI

A105128 Primes of the form 64n+33.

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Magma

Mathematica

A105130 Primes of the form 256n+129.

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Magma

Mathematica

A105134 Numbers n such that 16n+9 is prime.

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Magma

Mathematica

PARI

A105138 Numbers n such that 256n+129 is prime.

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Programs

Magma

Mathematica

PARI

A105139 Numbers k such that 512*k+257 is prime.

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Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A105135 Numbers n such that 32n+17 is prime.

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