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.

A187605 Primes of the form k^k + k - 1.

Original entry on oeis.org

5, 29, 1978419655660313589123997, 205891132094649000000000000000000000000000029
Offset: 1

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Author

Marco Ripà, Mar 11 2011

Keywords

Comments

See A058912 for numbers k such that k^k + k - 1 is prime. Subsequence of A231712 (numbers n^n + n - 1). - Jaroslav Krizek, Nov 13 2013
The next prime has 1460 digits. - Jinyuan Wang, Mar 01 2020

Crossrefs

Programs

  • Mathematica
    Do[p=n^n+n-1; If[PrimeQ[p], Print[p]], {n, 100}]
  • PARI
    lista(nn) = for(k=1, nn, if(ispseudoprime(q=k^k+k-1), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 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

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

A065798 Numbers k such that k^k - k - 1 is prime.

Original entry on oeis.org

3, 4, 5, 6, 9, 17, 22, 85, 710, 844, 1379
Offset: 1

Views

Author

Robert G. Wilson v, Dec 05 2001

Keywords

Comments

There is no further term up to 3000. - Farideh Firoozbakht, Oct 19 2006
a(12) > 20000. - User "Someone", added by Dmitry Petukhov, Sep 09 2021
If it exists, a(12) > 40000. - Dmitry Petukhov, Sep 12 2021

Crossrefs

Cf. A058912 (k^k+k-1).

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, May 22 2017

Extensions

a(9)-a(11) from Farideh Firoozbakht, Oct 19 2006

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.