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 1-6 of 6 results.

A058912 Numbers k such that k^k + k - 1 is prime.

Original entry on oeis.org

2, 3, 19, 30, 535, 1551, 7069, 8508
Offset: 1

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Author

Felice Russo, Jan 10 2001

Keywords

Comments

Except for the first term all terms are of the form 3k or 3k+1. - Farideh Firoozbakht, Oct 18 2006
Corresponding values of primes are in A187605. - Jaroslav Krizek, Nov 14 2013
If it exists, a(9) > 16100. - Hugo Pfoertner, Mar 02 2020
If it exists, a(9) > 31100. - Dmitry Petukhov, Sep 14 2021

Examples

			3 is a term because 3^3 + 3 - 1 = 29.
		

Crossrefs

Cf. A058911 (k^k + k + 1 is prime), A187605 (corresponding primes).

Programs

  • Mathematica
    Do[ If[ PrimeQ[ n^n + n - 1], Print[n]], {n, 1, 750} ]
  • PARI
    is(n)=ispseudoprime(n^n+n-1) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

a(6) from Farideh Firoozbakht, Oct 18 2006
a(7)-a(8) from Hugo Pfoertner, Mar 02 2020

A231712 a(n) = n^n + n - 1.

Original entry on oeis.org

0, 1, 5, 29, 259, 3129, 46661, 823549, 16777223, 387420497, 10000000009, 285311670621, 8916100448267, 302875106592265, 11112006825558029, 437893890380859389, 18446744073709551631, 827240261886336764193, 39346408075296537575441, 1978419655660313589123997
Offset: 0

Views

Author

Jaroslav Krizek, Nov 12 2013

Keywords

Comments

Supersequence of A187605 (primes of the form n^n + n - 1).
Numbers n such that a(n) = prime: 2, 3, 19, 30, 535, 1551, ..., another term > 2300 (see A058912 and A187605).
Also generalization of the problem: "What is the minimum length of a text consisting only of the first n letters of the alphabet and containing all possible n-tuples (no blanks)?" (see Puzzleup link). Example for n = 3, length of text a(3) = 29: AAABAACABBABCACBACCBBBCBCCCAA, all triples (AAA, AAB, ..., CCC) occurring exactly once. - Jörg Zurkirchen, Sep 06 2014

Crossrefs

Programs

Formula

a(n) = A066279(n) - 2 = A066068(n) - 1.
E.g.f.: 1/(1 + LambertW(-x)) + (x-1)*exp(x). - Alois P. Heinz, Jun 15 2018

A161471 Primes of the form k^k + k + 1.

Original entry on oeis.org

2, 3, 7, 31, 46663, 387420499
Offset: 1

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Author

Keywords

Comments

The associated k are in A058911. - R. J. Mathar, Jun 12 2009
a(7) = 116035988662615798148247830...0301775295923724561430603629007 (1232 digits).

Crossrefs

Programs

  • Mathematica
    Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; lst={}; Do[p=n^n+n+1; If[PrimeQ[p], AppendTo[lst,p]], {n,0,100}]; lst
    Join[{2},Select[Table[k^k+k+1,{k,1000}],PrimeQ]] (* Harvey P. Dale, Oct 09 2022 *)
  • PARI
    lista(nn) = for(k=0, nn, if(ispseudoprime(q=k^k+k+1), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 2020

Formula

Intersection of A000040 and A066279. - R. J. Mathar, Jun 12 2009

Extensions

Definition simplified by R. J. Mathar, Jun 12 2009

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

A357055 Integers k such that k^k + k^2 + 3*k + 2 is prime.

Original entry on oeis.org

0, 1, 3, 5, 11, 209, 1281
Offset: 1

Views

Author

Marco Ripà, Sep 10 2022

Keywords

Comments

a(8) > 20000, if it exists. - Michael S. Branicky, Sep 17 2024

Examples

			For k = 3, k^k + k^2 + 3*k + 2 = 47 and 47 is prime.
		

Crossrefs

Programs

  • PARI
    isok(k) = ispseudoprime(k^k + k^2 + 3*k + 2); \\ Michel Marcus, Sep 10 2022

A357056 Integers k such that k^k + k^2 + 2*k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 9, 10, 13, 15, 24
Offset: 1

Views

Author

Marco Ripà, Sep 10 2022

Keywords

Comments

The next prime (if any) is unknown, but it must exceed 2000^2000 + 2000^2 + 2*2000 + 1 (a 6603-digit number).
a(11) > 15000, if it exists. - Michael S. Branicky, Sep 17 2024

Examples

			If k = 2, then k^k + k^2 + k*2 + 1 = 2^2 + 2^2 + 2*2 + 1 = 13, which is prime.
		

Crossrefs

Showing 1-6 of 6 results.