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.

A058911 Numbers k such that k^k + k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 462
Offset: 1

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Author

Felice Russo, Jan 10 2001

Keywords

Comments

There is no further term up to 10000. - Farideh Firoozbakht, Nov 11 2006
If it exists, a(8) > 32100. - Dmitry Petukhov, Sep 14 2021

Examples

			a(2) = 2 because 2^2 + 2 + 1 = 7.
		

Crossrefs

Cf. A058912 (k^k + k - 1 is prime), A161471 (corresponding primes).

Programs

  • Mathematica
    Do[ If[ PrimeQ[ n^n + n + 1], Print[n]], {n, 1, 700} ]
    Join[{0},Select[Range[470],PrimeQ[#^#+#+1]&]] (* Harvey P. Dale, Dec 11 2022 *)
  • PARI
    f2(n,k) = for(x=1,n,y=x^x+x+k;if(ispseudoprime(y),print1(x","))) \\ Cino Hilliard, Jan 07 2005
    
  • PFGW
    ABC2 $a^$a + $a + 1
    a: from 0 to 1000 // Jinyuan Wang, Mar 01 2020

A182383 Primes of the form k^k - k + 1.

Original entry on oeis.org

2, 3, 3121, 302875106592241
Offset: 1

Views

Author

Alex Ratushnyak, Apr 27 2012

Keywords

Comments

The next term has 340 digits. - T. D. Noe, Apr 27 2012
a(6) is too large to include in the b-file. - Pontus von Brömssen, Aug 11 2025

Examples

			a(2) = 5^5 - 5 + 1 = 3125 - 4 = 3121.
		

Crossrefs

Cf. A065797 (corresponding values of k, except k=0), A161471, A161472.

Programs

  • Mathematica
    Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; Select[Table[n^n - n + 1, {n, 0, 100}], PrimeQ] (* T. D. Noe, Apr 27 2012 *)

A268987 Primes of the form k^(k + 1) + k - 1.

Original entry on oeis.org

83, 15629, 279941, 3486784409, 6568408355712890639
Offset: 1

Views

Author

Soumadeep Ghosh, Feb 16 2016

Keywords

Comments

The next prime has 171 digits. - Vincenzo Librandi, Feb 17 2016
Subsequence of primes of A155499. - Michel Marcus, Feb 20 2016

Crossrefs

Cf. A309140 (the corresponding values of k).

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is n^(n+1)+n-1]; // Vincenzo Librandi, Feb 17 2016
    
  • Mathematica
    Select[Table[n^(n + 1) + n - 1, {n, 1, 50}], ProvablePrimeQ[#] &]
  • PARI
    lista(nn) = for(k=1, nn, if(ispseudoprime(q=k^(k+1)+k-1), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 2020

A267014 Primes of the form a^a + a*b + b^b.

Original entry on oeis.org

2, 3, 5, 7, 23, 31, 37, 251, 257, 3119, 3167, 46649, 46663, 49811, 823591, 870241, 16780381, 387420479, 387420499, 285311717333, 11414881932150451, 18446744359021222403, 827240261886336764159, 827240261886336767387, 827240261886337587839, 827240261896336764347
Offset: 1

Views

Author

Altug Alkan, Jan 08 2016

Keywords

Comments

A161471 and A161472 are obvious subsequences.

Examples

			23 is a term because 3^3 + 3*(-1) + (-1)^(-1) = 23 is prime.
31 is a term because 3^3 + 3*1 + 1^1 = 31 is prime.
37 is a term because 3^3 + 3*2 + 2^2 = 37 is prime.
		

Crossrefs

Showing 1-4 of 4 results.