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 16 results. Next

A139487 Numbers k such that 8k + 7 is prime.

Original entry on oeis.org

0, 2, 3, 5, 8, 9, 12, 15, 18, 20, 23, 24, 27, 29, 32, 33, 38, 44, 45, 47, 53, 54, 57, 59, 60, 62, 74, 75, 78, 80, 89, 90, 92, 93, 102, 104, 107, 110, 113, 114, 120, 122, 123, 128, 129, 132, 135, 137, 143, 152, 153, 159, 162, 164, 165, 170, 174, 177, 179, 180, 183, 185
Offset: 1

Views

Author

Artur Jasinski, Apr 23 2008

Keywords

Comments

For numbers k such that:
8k+1 is prime see A005123, primes see A007519;
8k+3 is prime see A005124, primes see A007520;
8k+5 is prime see A105133, primes see A007521;
8k+7 is prime see A139487, primes see A007522.
8k + 7 divides A000225(4k+3). - Jinyuan Wang, Mar 08 2019

Links

Crossrefs

Cf. A000225, A007519, A007520, A007521, A007522, A005123, A005124, A105133.

Programs

  • Magma
    [n: n in [0..200] | IsPrime(8*n+7)]; // Vincenzo Librandi, Jun 25 2014
  • Mathematica
    a = {}; Do[If[PrimeQ[8 n + 7], AppendTo[a, n]], {n, 0, 300}]; a
Select[Range[0,200],PrimeQ[8#+7]&] (* Harvey P. Dale, Oct 10 2012 *)
  • PARI
    is(n)=isprime(8*n+7) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = (A007522(n) - 7)/8, n >= 1.

A023230 Numbers k such that k and 8*k + 5 are both prime.

Original entry on oeis.org

3, 7, 13, 19, 43, 67, 103, 109, 127, 139, 151, 181, 193, 199, 211, 223, 241, 277, 283, 349, 379, 397, 421, 433, 439, 463, 577, 601, 607, 613, 619, 727, 733, 787, 829, 853, 883, 967, 991, 1033, 1039, 1117, 1201, 1237, 1291, 1303, 1399, 1429, 1459, 1531, 1567, 1579
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A007521 (primes of form 8n+5), A105133 (numbers n such that 8n+5 is prime).

Programs

A105140 Numbers n such that 1024n+513 is prime.

Original entry on oeis.org

7, 10, 11, 17, 22, 25, 31, 35, 44, 50, 65, 74, 79, 82, 85, 94, 100, 109, 110, 112, 115, 116, 122, 130, 140, 149, 151, 154, 155, 157, 164, 166, 172, 179, 206, 211, 214, 215, 221, 227, 229, 232, 245, 254, 256, 259, 269, 271, 277, 280, 281, 292, 295, 296, 299, 316, 322, 332
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A095278, A105133-A105139, A002145, A007521, A105126-A105132.

Programs

A023262 Primes that remain prime through 2 iterations of the function f(x) = 8*x + 5.

Original entry on oeis.org

13, 43, 103, 139, 199, 349, 397, 577, 727, 733, 829, 967, 1039, 1303, 1567, 1597, 1753, 2131, 2161, 2311, 2707, 2719, 2857, 3109, 3319, 3613, 3673, 3697, 3853, 4051, 4129, 4201, 4297, 4441, 4507, 4513, 4639, 4663, 4789, 5503, 5701, 5743, 5857, 5953, 6121
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5 and 64*p+45 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023230, A105133.

Programs

  • Magma
    [n: n in [1..100000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45)] // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 16 2016

A023293 Primes that remain prime through 3 iterations of function f(x) = 8x + 5.

Original entry on oeis.org

43, 103, 199, 1039, 1303, 2311, 2857, 3673, 4513, 4663, 5743, 5953, 8431, 9721, 12391, 14143, 14533, 17599, 18457, 19507, 21211, 23719, 24169, 25621, 28663, 29023, 31963, 33409, 35311, 36979, 37423, 40867, 40939, 43891, 44371, 44983, 45841, 46747, 46807
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5, 64*p+45 and 512*p+365 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023230, A023262, and A105133.

Programs

  • Magma
    [n: n in [1..450000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45) and IsPrime(512*n+365)]; // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Prime[Range[5000]],AllTrue[Rest[NestList[8#+5&,#,3]],PrimeQ]&] (* Harvey P. Dale, Sep 19 2022 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 23 2016

A023321 Primes that remain prime through 4 iterations of function f(x) = 8x + 5.

Original entry on oeis.org

8431, 9721, 24169, 35311, 63577, 74203, 109471, 109891, 140269, 174613, 176599, 182857, 210187, 241561, 270553, 274837, 274909, 276517, 281557, 324763, 326737, 383659, 464089, 474127, 489109, 498403, 540781, 563587, 576943, 582949, 633253
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5, 64*p+45, 512*p+365 and 4096*p+2925 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023230, A023262, A023293, and A105133.

Programs

  • Magma
    [n: n in [1..5000000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45) and IsPrime(512*n+365) and IsPrime(4096*n+2925)] // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 19 or 31 (mod 42). - John Cerkan, Oct 08 2016

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

Views

Author

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

Keywords

Links

Crossrefs

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

Programs

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

Views

Author

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

Keywords

Links

Crossrefs

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

Programs

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

Views

Author

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

Keywords

Links

Crossrefs

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

Programs

A023349 Primes that remain prime through 5 iterations of function f(x) = 8x + 5.

Original entry on oeis.org

109891, 324763, 852367, 3371527, 3557797, 4448701, 4471549, 5304661, 5616679, 5688919, 5727349, 7766659, 8028109, 8554999, 9034723, 10867099, 11146987, 12396487, 12926401, 14186611, 18274513, 19251517, 20882713, 21810493, 23953921
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 8*p+5, 64*p+45, 512*p+365, 4096*p+2925 and 32768*p+23405 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023230, A023262, A023293, A023321, and A105133.

Programs

  • Magma
    [n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45) and IsPrime(512*n+365) and IsPrime(4096*n+2925) and IsPrime(32768*n+23405)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    p5Q[n_]:=And@@PrimeQ/@NestList[8#+5&,n,5]; Parallelize[Select[Prime[Range[1510000]],p5Q]] (* Harvey P. Dale, Feb 22 2011 *)

Formula

a(n) == 19 (mod 42). - John Cerkan, Nov 06 2016
Showing 1-10 of 16 results. Next

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

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