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 1-8 of 8 results.

A237810 Primes p such that 2*p+1 and 2*p+7 are also prime.

Original entry on oeis.org

2, 3, 5, 11, 23, 41, 53, 83, 113, 131, 173, 191, 251, 281, 293, 593, 641, 683, 743, 953, 1031, 1103, 1451, 1481, 1601, 2003, 2063, 2141, 2393, 2693, 2903, 3023, 3413, 3593, 3623, 3761, 3821, 3911, 4211, 4373, 4481, 4733, 4871, 5081, 5303, 5441, 5741, 5903
Offset: 1

Views

Author

Colin Barker, Feb 13 2014

Keywords

Examples

			11 is in the sequence because 11, 2*11+1 = 23 and 2*11+7 = 29 are all prime.

Links

Crossrefs

Cf. A126107, A237811, A237812, A237813, A237814.

Programs

  • Magma
    [p: p in PrimesUpTo(9200) | IsPrime(2*p+1) and IsPrime(2*p+7)]; // Vincenzo Librandi, Feb 15 2014
  • Mathematica
    Select[Prime[Range[10000]], PrimeQ[2 # + 1]&&PrimeQ[2 # + 7]&] (* Vincenzo Librandi, Feb 15 2014 *)
  • PARI
    s=[]; forprime(p=2, 10000, if(isprime(2*p+1) && isprime(2*p+7), s=concat(s, p))); s

A237811 Primes p such that 2*p+1 and 2*p+9 are also prime.

Original entry on oeis.org

2, 5, 11, 29, 131, 179, 239, 281, 359, 491, 641, 659, 719, 761, 809, 911, 1229, 1439, 1481, 1811, 2549, 2699, 2819, 3299, 3449, 3491, 4211, 4349, 4481, 5051, 5279, 5441, 5639, 5741, 6101, 6269, 6449, 6581, 6899, 7121, 7211, 7541, 7649, 7691, 8111, 8741, 8951
Offset: 1

Views

Author

Colin Barker, Feb 13 2014

Keywords

Examples

			11 is in the sequence because 11, 2*11+1 = 23 and 2*11+9 = 31 are all prime.

Links

Crossrefs

Cf. A126107, A237810, A237812, A237813, A237814.

Programs

  • Magma
    [p: p in PrimesUpTo(9200) | IsPrime(2*p+1) and IsPrime(2*p+9)]; // Vincenzo Librandi, Feb 15 2014
  • Mathematica
    Select[Prime[Range[10000]], PrimeQ[2 # + 1]&&PrimeQ[2 # + 9]&] (* Vincenzo Librandi, Feb 15 2014 *)
  • PARI
    s=[]; forprime(p=2, 10000, if(isprime(2*p+1) && isprime(2*p+9), s=concat(s, p))); s

A237812 Primes p such that 2*p+1 and 2*p+13 are also prime.

Original entry on oeis.org

2, 3, 5, 23, 29, 83, 89, 113, 173, 233, 239, 293, 509, 653, 719, 743, 1013, 1049, 1223, 1289, 1499, 2003, 2039, 2063, 2129, 2339, 2393, 2459, 2543, 2693, 2753, 2819, 2963, 3389, 3449, 4409, 4733, 4919, 5039, 6053, 6113, 6263, 6323, 6329, 6449, 7433, 7643
Offset: 1

Views

Author

Colin Barker, Feb 13 2014

Keywords

Examples

			23 is in the sequence because 23, 2*23+1 = 47 and 2*23+13 = 59 are all prime.

Links

Crossrefs

Cf. A126107, A237810, A237811, A237813, A237814.

Programs

  • Magma
    [p: p in PrimesUpTo(9200) | IsPrime(2*p+1) and IsPrime(2*p+13)]; // Vincenzo Librandi, Feb 15 2014
  • Mathematica
    Select[Prime[Range[10000]], PrimeQ[2 # + 1] && PrimeQ[2 # + 13] &] (* Vincenzo Librandi, Feb 15 2014 *)
Select[Prime[Range[1000]],AllTrue[2#+{1,13},PrimeQ]&] (* Harvey P. Dale, Jun 27 2023 *)
  • PARI
    s=[]; forprime(p=2, 10000, if(isprime(2*p+1) && isprime(2*p+13), s=concat(s, p))); s

A237813 Primes p such that 2*p+1 and 2*p+15 are also prime.

Original entry on oeis.org

2, 11, 23, 29, 41, 83, 89, 113, 131, 179, 191, 281, 293, 359, 419, 431, 491, 509, 593, 641, 653, 683, 719, 1019, 1049, 1103, 1229, 1289, 1409, 1451, 1511, 1583, 1601, 1811, 1889, 1931, 2003, 2039, 2069, 2129, 2141, 2273, 2393, 2399, 2459, 2543, 2549, 2699
Offset: 1

Views

Author

Colin Barker, Feb 13 2014

Keywords

Examples

			11 is in the sequence because 11, 2*11+1 = 23 and 2*11+15 = 37 are all prime.

Links

Crossrefs

Cf. A126107, A237810, A237811, A237812, A237814.

Programs

  • Magma
    [p: p in PrimesUpTo(4000) | IsPrime(2*p+1) and IsPrime(2*p+15)]; // Vincenzo Librandi, Feb 15 2014
  • Mathematica
    Select[Prime[Range[5000]], PrimeQ[2 # + 1] && PrimeQ[2 # + 15] &] (* Vincenzo Librandi, Feb 15 2014 *)
  • PARI
    s=[]; forprime(p=2, 10000, if(isprime(2*p+1) && isprime(2*p+15), s=concat(s, p))); s

A237814 Primes p such that 2*p+1 and 2*p+19 are also prime.

Original entry on oeis.org

2, 5, 11, 41, 89, 131, 191, 251, 419, 431, 641, 809, 1031, 1229, 1409, 1439, 1511, 1559, 1601, 1889, 1901, 1931, 2069, 2351, 2399, 2459, 2699, 2741, 2819, 2939, 3359, 3449, 3491, 3761, 3779, 3911, 4409, 4919, 5081, 5849, 6131, 6449, 6491, 6551, 7079, 7151
Offset: 1

Views

Author

Colin Barker, Feb 13 2014

Keywords

Examples

			11 is in the sequence because 11, 2*11+1 = 23 and 2*11+19 = 41 are all prime.

Links

Crossrefs

Cf. A126107, A237810, A237811, A237812, A237813.

Programs

  • Magma
    [p: p in PrimesUpTo(8000) | IsPrime(2*p+1) and IsPrime(2*p+19)]; // Vincenzo Librandi, Feb 15 2014
  • Mathematica
    Select[Prime[Range[8000]], PrimeQ[2 # + 1] && PrimeQ[2 # + 19] &] (* Vincenzo Librandi, Feb 15 2014 *)
  • PARI
    s=[]; forprime(p=2, 10000, if(isprime(2*p+1) && isprime(2*p+19), s=concat(s, p))); s

A230117 Primes p such that 2*p+1 is prime and 2*p+3 is not prime.

Original entry on oeis.org

3, 11, 23, 41, 83, 131, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 593, 641, 653, 683, 719, 761, 911, 953, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1511, 1601, 1811, 1889, 1901, 1931, 1973, 2003, 2039, 2069, 2141
Offset: 1

Views

Author

Vincenzo Librandi, Oct 10 2013

Keywords

Comments

Intersection of A005384 and A163769. - Felix Fröhlich, Jan 14 2017

Examples

			23 is in the sequence because 2*23+1=47 (prime) and 2*23+3=49 (not prime).

Links

Crossrefs

Cf. A005384, A023204, A053176, A126107, A163769, A230039.

Programs

  • Magma
    [p: p in PrimesUpTo(2500)| IsPrime(2*p+1) and not IsPrime(2*p+3)];
  • Mathematica
    Select[Range[10^6],PrimeQ[#]&& PrimeQ[2#+1]&&!PrimeQ[2#+3]&]
  • PARI
    is(n) = ispseudoprime(n) && ispseudoprime(2*n+1) && !ispseudoprime(2*n+3) \\ Felix Fröhlich, Jan 14 2017

A230039 Primes p such that 2*p+1 is not prime and 2*p+3 is prime.

Original entry on oeis.org

7, 13, 17, 19, 43, 47, 67, 73, 97, 127, 137, 139, 157, 167, 193, 197, 199, 223, 227, 229, 269, 277, 283, 307, 337, 349, 353, 379, 383, 397, 409, 439, 463, 467, 487, 503, 523, 547, 557, 563, 599, 607, 613, 617, 643, 647, 739, 773, 797, 827, 853, 859, 887, 929
Offset: 1

Views

Author

Vincenzo Librandi, Oct 10 2013

Keywords

Comments

Intersection of A023204 and A053176. - Felix Fröhlich, Jan 14 2017

Examples

			43 is in the sequence because 2*43+1=87 (not prime) and 2*43+3=89 (prime).

Links

Crossrefs

Cf. A005384, A023204, A053176, A126107, A163769, A230117.

Programs

  • Magma
    [p: p in PrimesUpTo(2500)|not IsPrime(2*p+1) and IsPrime(2*p+3)];
  • Mathematica
    Select[Range[10^5],PrimeQ[#]&& !PrimeQ[2#+1]&& PrimeQ[2#+3]&]
  • PARI
    is(n) = ispseudoprime(n) && !ispseudoprime(2*n+1) && ispseudoprime(2*n+3) \\ Felix Fröhlich, Jan 14 2017

A230225 Primes p such that 2*p+1 and 2*p+3 are not prime.

Original entry on oeis.org

31, 37, 59, 61, 71, 79, 101, 103, 107, 109, 149, 151, 163, 181, 211, 241, 257, 263, 271, 311, 313, 317, 331, 347, 367, 373, 389, 401, 421, 433, 449, 457, 461, 479, 499, 521, 541, 569, 571, 577, 587, 601, 619, 631, 661, 673, 677, 691, 701, 709, 727, 733, 751
Offset: 1

Views

Author

Vincenzo Librandi, Oct 12 2013

Keywords

Examples

			31 is in the sequence because 2*31+1=63 and 2*31+3=65 are not prime.

Links

Crossrefs

Cf. A005384, A023204, A053176, A089531, A126107, A163769, A230039, A230117.

Programs

  • Magma
    [p: p in PrimesUpTo(2500)|not IsPrime(2*p+1) and not IsPrime(2*p+3)];
  • Mathematica
    Select[Range[10^3], PrimeQ[#]&&!PrimeQ[2 # + 1]&&!PrimeQ[2 # + 3]&]
Select[Prime[Range[200]],NoneTrue[2#+{1,3},PrimeQ]&] (* Harvey P. Dale, Sep 19 2021 *)
Showing 1-8 of 8 results.

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

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