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.

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).
Cf. A110932, A062207, A108318.

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

A302134 Numbers k such that 9*k^k - 8 is prime.

Original entry on oeis.org

7, 9, 11, 353, 7133
Offset: 1

Views

Author

Seiichi Manyama, Apr 02 2018

Keywords

Comments

9*353^353 - 8 is a probable prime.

Crossrefs

Numbers k such that b*k^k - b + 1 is prime: A110931 (b=2), A302132 (b=3), A301521 (b=4), A302123 (b=6), A302133 (b=8), this sequence (b=9), A302136 (b=10).

Programs

  • PARI
    isok(k) = ispseudoprime(9*k^k - 8); \\ Altug Alkan, Apr 02 2018

Extensions

a(5) from Michael S. Branicky, Apr 15 2023

A302136 Numbers k such that 10*k^k - 9 is prime.

Original entry on oeis.org

2, 4, 14, 80, 1133, 4120
Offset: 1

Views

Author

Seiichi Manyama, Apr 02 2018

Keywords

Comments

10*1133^1133 - 9 is a probable prime.
a(6) > 3000. - Tyler NeSmith, May 15 2021
a(7) > 20000. - Michael S. Branicky, Nov 29 2024

Crossrefs

Numbers k such that b*k^k - b + 1 is prime: A110931 (b=2), A302132 (b=3), A301521 (b=4), A302123 (b=6), A302133 (b=8), A302134 (b=9), this sequence (b=10).
Cf. A302137.

Programs

  • PARI
    isok(k) = ispseudoprime(10*k^k - 9); \\ Altug Alkan, Apr 02 2018

Extensions

a(6) from Michael S. Branicky, Mar 28 2023

A302124 Primes of form 6*k^k - 5.

Original entry on oeis.org

19, 157, 1531, 4941253, 100663291, 2324522929, 774660240526566167037696179607987213236023100283073
Offset: 1

Views

Author

Seiichi Manyama, Apr 01 2018

Keywords

Comments

The next term is too large to include.
The next term has 297 digits. - Harvey P. Dale, May 24 2021

Crossrefs

Primes of form b*k^k - b + 1: A301870 (b=4), this sequence (b=6).
Cf. A302091, A302123.

Programs

  • Mathematica
    Select[Table[6k^k-5,{k,50}],PrimeQ] (* Harvey P. Dale, May 24 2021 *)

Formula

a(n) = 6*A302123(n)^A302123(n) - 5.

A302132 Numbers k such that 3*k^k - 2 is prime.

Original entry on oeis.org

3, 1571, 2601
Offset: 1

Views

Author

Seiichi Manyama, Apr 02 2018

Keywords

Comments

The terms greater than or equal to 1571 correspond to probable primes.
a(4) > 25000, if it exists. - Michael S. Branicky, Sep 02 2024

Crossrefs

Numbers k such that b*k^k - b + 1 is prime: A110931 (b=2), this sequence (b=3), A301521 (b=4), A302123 (b=6), A302133 (b=8), A302134 (b=9), A302136 (b=10).

Programs

  • PARI
    isok(k) = ispseudoprime(3*k^k - 2); \\ Altug Alkan, Apr 02 2018

A302133 Numbers k such that 8*k^k - 7 is prime.

Original entry on oeis.org

10, 800, 1266, 1395
Offset: 1

Views

Author

Seiichi Manyama, Apr 02 2018

Keywords

Comments

The terms greater than or equal to 800 correspond to probable primes.
a(5) > 4000. - Tyler NeSmith, May 13 2021
a(5) > 20000. - Michael S. Branicky, Sep 02 2024

Crossrefs

Numbers k such that b*k^k - b + 1 is prime: A110931 (b=2), A302132 (b=3), A301521 (b=4), A302123 (b=6), this sequence (b=8), A302134 (b=9), A302136 (b=10).

Programs

  • PARI
    isok(k) = ispseudoprime(8*k^k - 7); \\ Altug Alkan, Apr 02 2018
Showing 1-6 of 6 results.

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