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 1-3 of 3 results.

A094475 Primes of form 2^n + 5^n.

Original entry on oeis.org

2, 7, 29, 641
Offset: 1

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Author

Labos Elemer, Jun 01 2004

Keywords

Comments

2^n+p^n is prime if n=0;or n=1 and p is a smaller of twin primes; or n=2 and 4+p^2 is prime; or n=3 and 8+p^3 is prime etc. Several conditions have to be satisfied to get a modest number of terms...
n must be zero or a power of two. Checked n being powers of two through 2^22. Thus a(5) > 10^5800000. Primes of this magnitude are rare (about 1 in 13.4 million), so chance of finding one is remote with today's computer algorithms and speeds. - Robert Price, May 02 2013

Examples

			For n=4, p=2^4+5^4=641, so p can be prime even when the exponent is not a prime.
		

Crossrefs

Programs

  • Magma
    [ a: n in [0..2100] | IsPrime(a) where a is 5^n+2^n]; // Vincenzo Librandi, Nov 18 2010
  • Mathematica
    Select[Table[2^n+5^n,{n,0,5000}],PrimeQ] (* Harvey P. Dale, May 28 2014 *)

A094477 Primes of form 2^n + 37^n.

Original entry on oeis.org

2, 1373, 1874177, 23169162752708970943114627382699355445603465075569066753527132965271355336698663708393617779709970177
Offset: 1

Views

Author

Labos Elemer, Jun 01 2004

Keywords

Comments

The number n must be zero or a power of 2. Checked n being powers of two through 2^20. Thus a(5) > 10^3200000. Primes of this magnitude are rare (about 1 in 7.5 million), so chance of finding one is remote with today's computer algorithms and speeds. - Robert Price, Apr 29 2013

Crossrefs

Extensions

No more terms for n < 1000, so the next term will be too large to include. - Hugo Pfoertner, Aug 17 2004

A386618 Primes of the form 2^k + 13^k.

Original entry on oeis.org

2, 173, 815730977
Offset: 1

Views

Author

Vincenzo Librandi, Aug 17 2025

Keywords

Comments

If 13^k + 2^k is prime then k is either 0 or a power of 2. The corresponding values of k for a(1)-a(4) are 0, 2, 8 and 512. The fourth value is too long to enter.

Crossrefs

Programs

  • Magma
    [a: n in [0..200] | IsPrime(a) where a is 13^n+2^n ];
  • Mathematica
    Select[Table[2^n+13^n,{n,0,600}],PrimeQ]
Showing 1-3 of 3 results.