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.

A110931 Numbers k such that 2*k^k - 1 is prime.

Original entry on oeis.org

2, 3, 357, 1400, 205731, 296598
Offset: 1

Views

Author

Ray G. Opao, Sep 25 2005

Keywords

Comments

a(5) > 4000. - Ray G. Opao, Oct 23 2014
a(5) > 101000. - Serge Batalov, Apr 13 2018

Examples

			3 is in the sequence since 2*3^3 - 1 = 53 is prime.
		

Crossrefs

Numbers k such that b*k^k - b + 1 is prime: this sequence (b=2), A301521 (b=4), A302123 (b=6).

Programs

  • Magma
    [n: n in [0..500] | IsPrime(2*n^n-1)]; // Vincenzo Librandi, Nov 01 2014
  • Mathematica
    Select[Range[1000], PrimeQ[2*#^# - 1] &] (* Vaclav Kotesovec, Oct 31 2014 *)
  • PARI
    for(n=1,2000,1;if(isprime(2*n^n-1),print(n))) \\ Ray G. Opao, Oct 23 2014
    

Extensions

a(5-6) from Ryan Propper, Jul 24-28 2022

A108879 Numbers n such that (n-1)*n^n+1 is prime.

Original entry on oeis.org

2, 4, 20, 93, 100, 1536, 2835
Offset: 1

Views

Author

Ray G. Opao, Jul 14 2005

Keywords

Examples

			2 is in the sequence because (2-1)*2^2+1 = 1*2^2+1 = 4+1 = 5, which is prime.
		

Crossrefs

Cf. A108318.

Programs

  • Magma
    [n: n in [1..1000] |IsPrime((n-1)*n^n+1)]; // Vincenzo Librandi, Oct 23 2014
    
  • Mathematica
    Select[Range[1000], PrimeQ[(# - 1) #^# + 1] &] (* Vincenzo Librandi, Oct 23 2014 *)
  • PARI
    isok(n) = isprime((n-1)*n^n+1); \\ Michel Marcus, Oct 23 2014
    
  • Python
    from sympy import isprime
    def afind(limit, startk=0):
        for k in range(startk, limit+1):
            if isprime((k-1)*k**k + 1):
                print(k, end=", ")
    afind(200) # Michael S. Branicky, Jan 01 2022

Extensions

a(7) from Michael S. Branicky, Jan 01 2022

A353122 Numbers k such that k^k*(k+1) + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 186, 198, 8390
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 24 2022

Keywords

Comments

Corresponding primes start 2, 3, 13, 109, 326593, 3874204891, ...
a(9) > 6000. - Jon E. Schoenfield, Jun 05 2022
a(10) > 18000. - Michael S. Branicky, Aug 08 2024

Examples

			9 is in the sequence because 9^9*(9+1) + 1 = 3874204891, which is prime.
		

Crossrefs

Programs

  • Magma
    [n: n in [0..200] | IsPrime(n^n*(n+1) + 1)];
    
  • Mathematica
    Join[{0}, Select[Range[200], PrimeQ[#^#*(# + 1) + 1] &]] (* Amiram Eldar, Apr 25 2022 *)
  • PARI
    isok(k) = ispseudoprime(k^k*(k+1) + 1); \\ Michel Marcus, May 16 2022

Extensions

a(9) from Michael S. Branicky, Dec 22 2023
Showing 1-3 of 3 results.