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 1-4 of 4 results.

A245241 Integers n such that 6 * 7^n + 1 is prime.

Original entry on oeis.org

0, 1, 4, 9, 99, 412, 2633, 5093, 5632, 28233, 36780, 47084, 53572
Offset: 1

Views

Author

Robert Price, Nov 14 2014

Keywords

Comments

All terms correspond to verified primes, that is, not merely probable primes.
a(14) > 2*10^5.

Examples

			4 is in this sequence because 6 * 7^4 + 1 = 14407, which is prime.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[0,200000], PrimeQ[6 * 7^# + 1] &]

A216889 Numbers k such that 12*3^k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 5, 13, 14, 38, 200, 248, 884, 1004, 1253, 1634, 3305, 3521, 9601, 19784, 72697
Offset: 1

Views

Author

Vincenzo Librandi, Sep 26 2012

Keywords

Comments

a(19) > 2*10^5. - Robert Price, Mar 16 2014
All terms are verified primes (i.e., not merely probable primes). - Robert Price, Mar 16 2014

Crossrefs

Programs

  • Magma
    [n: n in [0..4000] | IsPrime(12*3^n + 1)];
    
  • Mathematica
    Select[Range[4000], PrimeQ[12 * 3^# + 1] &]
  • PARI
    is(n)=ispseudoprime(12*3^n+1) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = A005537(n+1) - 1. - Bruno Berselli, Sep 27 2012

Extensions

a(16)-a(17) from Vincenzo Librandi, Sep 30 2012
a(18) from Robert Price, Mar 16 2014

A216890 Numbers n such that 14*3^n + 1 is prime.

Original entry on oeis.org

1, 2, 3, 18, 22, 26, 27, 33, 39, 57, 62, 94, 145, 246, 390, 398, 402, 571, 690, 906, 1062, 1254, 1367, 1627, 1954, 2409, 3107, 14754, 15378, 24219, 46138, 98883, 161178
Offset: 1

Views

Author

Vincenzo Librandi, Sep 26 2012

Keywords

Comments

The next terms are > 6000.
a(34) > 2*10^5. - Robert Price, Mar 16 2014
All terms are verified primes (i.e., not probable primes). - Robert Price, Mar 16 2014

Crossrefs

Programs

  • Magma
    [n: n in [0..4000] | IsPrime(14*3^n+1)];
    
  • Mathematica
    Select[Range[4000], PrimeQ[14 3^# + 1] &]
  • PARI
    is(n)=ispseudoprime(14*3^n+1) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(28)-a(33) from Robert Price, Mar 16 2014

A216888 Numbers k such that 6*3^k + 1 is prime.

Original entry on oeis.org

0, 1, 3, 4, 5, 8, 15, 16, 29, 53, 56, 59, 64, 131, 179, 319, 695, 781, 821, 896, 1251, 1453, 4216, 5479, 6224, 7841, 12095, 13781, 17719, 43955, 64821, 82779, 105105, 152528, 165895, 191813, 529679, 1074725, 1086111, 1175231, 1277861, 1346541, 3123035, 3648968, 5570080, 6236771, 10852676
Offset: 1

Views

Author

Vincenzo Librandi, Sep 26 2012

Keywords

Examples

			3 is a term because 6*3^3 + 1 = 163 is prime.
7 is not a term because 6*3^7 + 1 = 13123 = 11*1193 is composite.
		

Crossrefs

Associated primes are in A111974.

Programs

  • Magma
    /* Gives only the terms up to 1453: */ [n: n in [0..1500] | IsPrime(6*3^n + 1)];
    
  • Mathematica
    Select[Range[5000], PrimeQ[6 3^# + 1] &]
  • PARI
    is(n)=ispseudoprime(6*3^n+1) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = A003306(n+1)-1. - Bruno Berselli, Sep 27 2012

Extensions

More terms from Vincenzo Librandi, Oct 01 2012
a(41)-a(47) from the data at A003306 added by Amiram Eldar, Jul 18 2025
Showing 1-4 of 4 results.