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.

A057909 Numbers k such that 4^k + k is prime.

Original entry on oeis.org

1, 3, 9, 15, 37, 85, 133, 225, 1233, 12793, 108889
Offset: 1

Views

Author

Robert G. Wilson v, Nov 16 2000

Keywords

Comments

a(11) > 20000. - Jinyuan Wang, Feb 01 2020

Crossrefs

Cf. A158879 (4^n + n).

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 4^n + n ], Print[ n ] ], {n, 0, 3000} ]
  • PARI
    is(n)=ispseudoprime(4^n+n) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(10) from Jinyuan Wang, Feb 01 2020
a(11) from Hugo Pfoertner, Mar 02 2024

A121823 (3^p+p)/(p+1) with (p + 1) odd prime > 3.

Original entry on oeis.org

17, 105, 5369, 40881, 2532161, 20390553, 1364393897, 788854912241, 6641649422409, 4056611764783761, 296528425830656801, 2544627654221217657, 188573151481968108425, 121907205457107043376081, 79832689783834658219010233, 694937020905183664168761201, 461241110188546453162994653785, 35255711337932980300219323747689
Offset: 1

Views

Author

Zak Seidov, Aug 27 2006

Keywords

Comments

See comments in A057900.

Examples

			a(1) = (3^4 + 4)/(4+1) = 17, a(2) = (3^6 + 6)/(6+1) = 105.
		

Crossrefs

Cf. A057900.

Programs

  • Maple
    map(t -> (3^(t-1)+t-1)/t, select(isprime,[seq(i,i=5..100,2)])); # Robert Israel, Nov 13 2017

Extensions

Corrected and edited according to suggestion of Michel Marcus by Zak Seidov, Oct 20 2013
More terms from Robert Israel, Nov 13 2017

A273942 Primes of the form 3^k + k.

Original entry on oeis.org

11, 6569, 16677181699666603
Offset: 1

Views

Author

Vincenzo Librandi, Jun 06 2016

Keywords

Comments

Terms given correspond to k in A057900.
a(4) has 731 digits.

Crossrefs

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is 3^n+n];
  • Mathematica
    Select[Table[3^n + n, {n, 1, 1000}], PrimeQ]

Formula

a(n) = A104743(A057900(n)). - Amiram Eldar, Jul 27 2025

A382786 Numbers k such that 5^k + k is prime.

Original entry on oeis.org

7954, 22102, 33054, 135156
Offset: 1

Views

Author

Nico Puada, Apr 24 2025

Keywords

Comments

All terms must end in the digit 2, 4, 6 or 8, otherwise 5^k + k is divisible by 2 or 5, which is not prime. - Jakub Buczak, May 04 2025

Crossrefs

Programs

  • Mathematica
    Select[Range[35000], PrimeQ[5^# + #] &] (* Nico Puada, Apr 24 2025 *)

Extensions

a(4) corrected by Jakub Buczak, May 04 2025
Showing 1-4 of 4 results.