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.

A262098 Primes p such that 2^p + 9 is also prime.

Original entry on oeis.org

2, 3, 5, 7, 23, 37, 47, 263, 317, 3229, 3253
Offset: 1

Views

Author

Vincenzo Librandi, Sep 18 2015

Keywords

Comments

a(12) > 100000. - Dana Jacobsen, Oct 03 2015
a(12) > 382198 using A057196. - Michael S. Branicky, Oct 31 2024

Examples

			5 is in sequence because 2^5 + 9 = 41 is prime.
		

Crossrefs

Subsequence of primes of A057196.
Cf. primes p such that 2^p+k is a prime: A057736 (k=3), A175173 (k=5), this sequence (k=9), A155780 (k=11), A175234 (k=15), A262099 (k=17), A175235 (k=21), A175236 (k=23), A262934 (k=27), A262100 (k=29), A262201 (k=33), A262962 (k=35).

Programs

  • Magma
    [p: p in PrimesUpTo(1000) | IsPrime(2^p+9)];
    
  • Mathematica
    Select[Prime[Range[1000]], PrimeQ[2^# + 9] &]
  • PARI
    for(n=1, 1e3, if(isprime((2^prime(n))+9), print1(prime(n)", "))) \\ Altug Alkan, Sep 18 2015
    
  • Perl
    use ntheory ":all"; use Math::GMP qw/:constant/; forprimes { say if is_prime(2**$+9) } 10000; # _Dana Jacobsen, Oct 03 2015

A057737 Primes of the form 2^p + 3, where p is prime.

Original entry on oeis.org

7, 11, 131, 147573952589676412931
Offset: 1

Views

Author

G. L. Honaker, Jr., Oct 29 2000

Keywords

Comments

The next term in the sequence is larger than 2^2741+3 > 10^825. - Philip Sung (philip_sung(AT)hotmail.com), Feb 02 2003
The next term in the sequence is larger than 2^100003+3 > 10^30104. - after Ryan Propper, Aug 24 2005

Crossrefs

Cf. A057736.

Programs

  • Mathematica
    Select[Table[2^p+3, {p, Prime[Range[67]]}], PrimeQ] (* Metin Sariyar, Aug 09 2019 *)
  • PARI
    forprime(p=1, , my(x=2^p+3); if(ispseudoprime(x), print1(x, ", "))) \\ Felix Fröhlich, Aug 09 2019

Formula

a(n) = 2^A057736(n) + 3. - Felix Fröhlich, Aug 09 2019

A153503 Primes p such that 2^(p-1)+3 is prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 19, 29, 31, 229, 2371, 4003, 33029, 55457, 58313, 205963, 1875553
Offset: 1

Views

Author

Vincenzo Librandi, Dec 28 2008

Keywords

Comments

A prime p is in the sequence if and only if p-1 is in A057732.

Examples

			For p = 2, 2^(p-1)+3 = 5 is prime.
For p = 17, 2^(p-1)+3 = 65539 is prime.
For p = 31, 2^(p-1)+3 = 1073741827 is prime.
		

Crossrefs

Cf. A057732 (numbers k such that 2^k + 3 is prime), A057736 (primes p such that 2^p + 3 is prime), A000043 (primes p such that 2^p - 1 is prime).

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | IsPrime(2^(p-1) + 3)]; // Vincenzo Librandi, Jun 09 2015
  • Mathematica
    Select[Prime[Range[3000]], PrimeQ[2^(# - 1) + 3] &] (* Vincenzo Librandi, Jun 09 2015 *)

Extensions

Edited and a(13)-a(15) (based on A057732) added by Klaus Brockhaus, Jan 06 2009
a(16) from Vincenzo Librandi, Jun 09 2015
a(17) from Amiram Eldar, Aug 01 2024

A229065 Numbers of the form 2^(p-1)+3, where p is prime.

Original entry on oeis.org

5, 7, 19, 67, 1027, 4099, 65539, 262147, 4194307, 268435459, 1073741827, 68719476739, 1099511627779, 4398046511107, 70368744177667, 4503599627370499, 288230376151711747, 1152921504606846979, 73786976294838206467, 1180591620717411303427, 4722366482869645213699
Offset: 1

Views

Author

Vincenzo Librandi, Sep 17 2013

Keywords

Comments

Primes in the sequence: 5, 7, 19, 67, 4099, 65539, 262147, 268435459, 1073741827, ...
On the other hand, for example, 2^(p-1) + 3 is composite when p == 11 (mod 12) or p == 5 (mod 18), with p>5; or when p is of the form 2*h^2+2*h*(k+2)+3*k, with k>0 and h>1.

Crossrefs

Cf. A153503 (associated primes p), A098828, A057732, A057736.

Programs

  • Magma
    [2^(p-1)+3:  p in PrimesUpTo(80)];
  • Mathematica
    Table[2^(Prime[n] - 1) + 3, {n, 25}]
Showing 1-4 of 4 results.