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.

A261577 Numbers m such that (4^m + 11) / 3 is prime.

Original entry on oeis.org

1, 4, 10, 34, 40, 106, 418, 682, 12702, 30484, 182026, 217720, 241306
Offset: 1

Views

Author

Vincenzo Librandi, Aug 26 2015

Keywords

Comments

From Bruno Berselli, Aug 26 2015: (Start)
After 1, m is always even (for m odd 4^m+11 is divisible by 5).
Let m = 2*h. For h = 3*k+1, 9*k+3, 11*k+2, 11*k+8, 13*k+8, 19*k+6, 23*k+10, 23*k+14 and 29*k+28, 4^m+11 is divisible by 9, 37, 89, 23, 53, 229, 47, 1013 and 59, respectively. (End)
All terms appear to be of the form 3*k+1. - Dhilan Lahoti, Aug 31 2015
12702 is the first counterexample to Dhilan Lahoti's conjecture: 12702 = 3*4234. - Bruno Berselli, Feb 02 2017
a(14) > 300,000. - Robert Price, Mar 18 2017

Examples

			4 is in the sequence because (4^4+11)/3 = 89 is prime.
10 is in the sequence because (4^10+11)/3 = 349529 is prime.
		

Crossrefs

Cf. A163868.
Cf. similar sequences listed in A261539.

Programs

  • Magma
    [n: n in [0..1500] | IsPrime((4^n+11) div 3)];
    
  • Mathematica
    Select[Range[0, 5000], PrimeQ[(4^# + 11)/3] &]
  • PARI
    is(n)=isprime((4^n + 11) / 3) \\ Anders Hellström, Aug 31 2015

Extensions

a(9)-a(12) from Robert Price, Feb 01 2017
a(13) from Robert Price, Mar 18 2017

A261578 Numbers m such that (4^m + 17) / 3 is prime.

Original entry on oeis.org

1, 2, 5, 8, 11, 23, 26, 59, 83, 89, 116, 1103, 1568, 5768, 13376, 17810, 18614, 66209, 167933, 188318
Offset: 1

Views

Author

Vincenzo Librandi, Aug 26 2015

Keywords

Comments

After 1, m is of the form 3*k+2. In fact, for m = 3*k or 3*k+1, 4^n+17 is divisible by 9 and 7, respectively. [Bruno Berselli, Aug 26 2015]
a(21) > 300000. - Robert Price, Apr 04 2017

Examples

			2 is in the sequence because (4^2+17)/3 = 11 is prime.
5 is in the sequence because (4^5+17)/3 = 347 is prime.
		

Crossrefs

Cf. similar sequences listed in A261539.

Programs

  • Magma
    [n: n in [0..1000] | IsPrime((4^n+17) div 3)];
    
  • Mathematica
    Select[Range[0, 5000], PrimeQ[(4^# + 17)/3] &]
  • PARI
    for(n=1, 1e3, if(isprime((4^n+17)/3), print1(n", "))) \\ Altug Alkan, Sep 14 2015

Extensions

a(14)-a(15) from Vincenzo Librandi, Sep 14 2015
a(16)-a(20) from Robert Price, Feb 01 2017

A261579 Numbers m such that (4^m + 23) / 3 is prime.

Original entry on oeis.org

2, 3, 5, 6, 27, 47, 66, 77, 83, 105, 197, 231, 293, 702, 1692, 3021, 6270, 6897, 7733, 14537, 15797, 21083, 21276, 28817, 65430, 111231, 137405, 141017, 185225
Offset: 1

Views

Author

Vincenzo Librandi, Aug 27 2015

Keywords

Comments

a(30) > 450,000. - Robert Price, Oct 04 2018

Examples

			2 is in the sequence because (4^2 + 23)/3 = 13 is prime.
3 is in the sequence because (4^3 + 23)/3 = 29 is prime.
		

Crossrefs

Cf. similar sequences listed in A261539.

Programs

  • Magma
    [n: n in [0..1500] | IsPrime((4^n+23) div 3)];
  • Mathematica
    Select[Range[0, 5000], PrimeQ[(4^# + 23)/3] &]

Extensions

a(17)-a(28) from Robert Price, Feb 01 2017
a(29) from Robert Price, Oct 04 2018

A273009 Numbers k such that (2^k + 5) / 3 is prime.

Original entry on oeis.org

0, 2, 4, 6, 12, 18, 24, 42, 84, 300, 390, 780, 822, 2430, 5508, 5514, 6492, 12372, 22680, 25770, 169416, 174240, 383544, 1007838, 1572882
Offset: 1

Views

Author

Vincenzo Librandi, May 13 2016

Keywords

Comments

Larger members of the sequence generate probable primes only.
Corresponding prime numbers are: 2, 3, 7, 23, 1367, 87383, 5592407, 1466015503703,6447604371278022265099607,.. etc.

Crossrefs

Cf. A261539.

Programs

  • Magma
    [n: n in [0..2000] | (2^n+5) mod 3 eq 0 and IsPrime((2^n+5) div 3)];
    
  • Mathematica
    Select[Range[0,10000], PrimeQ[(2^# + 5)/3] &]
  • PARI
    is(n)=ispseudoprime((2^n+5)/3) \\ Charles R Greathouse IV, Jun 07 2016

Formula

a(n) = 2*A261539(n).
Showing 1-4 of 4 results.