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 1-7 of 7 results.

A110932 Numbers k such that 2*k^k + 1 is prime.

Original entry on oeis.org

0, 1, 12, 18, 251, 82992
Offset: 0

Views

Author

Ray G. Opao, Sep 25 2005

Keywords

Comments

As a "list of numbers such that ...", the sequence should have offset 1, but to preserve the validity of formulas referring to this sequence, the offset was set to 0 when the initial value a(0)=0 was added. - M. F. Hasler, Sep 02 2012

Crossrefs

Cf. A110931, A121270 (= primes in A014566), A088790, A160360, A160600.
The primes 2n^n+1, for k<4, n=a(k)<251, are listed at A216148(k) = A216147(a(k)). - M. F. Hasler, Sep 02 2012

Programs

  • Mathematica
    Join[{0}, Select[Range[1000], PrimeQ[2*#^# + 1] &]] (* Robert Price, Mar 27 2019 *)
  • PARI
    is_A110932(n)=ispseudoprime(n^n*2+1) \\ M. F. Hasler, Sep 02 2012

Extensions

a(5) from Serge Batalov, Apr 08 2018

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

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

A301524 Numbers k such that 16*k^k - 1 is prime.

Original entry on oeis.org

3, 5, 15, 27
Offset: 1

Views

Author

Seiichi Manyama, Mar 23 2018

Keywords

Comments

All terms are odd since 16*(2*m)^(2*m) - 1 = (2^(m+2)*m^m - 1)*(2^(m+2)*m^m + 1). - Altug Alkan, Mar 23 2018
a(5), if it exists, is greater than 5000. - Vaclav Kotesovec, Mar 25 2018
a(5), if it exists, is greater than 20000. - Michael S. Branicky, Sep 03 2024

Crossrefs

Cf. A110931, A301522.

Programs

  • Mathematica
    Select[Range[1000], PrimeQ[16*#^# - 1] &] (* Vaclav Kotesovec, Mar 25 2018 *)
  • PARI
    for(n=0, 1000, if(isprime(16*n^n-1), print1(n", ")))

A118305 Numbers k such that 3*k^k-1 is prime.

Original entry on oeis.org

1, 2, 6, 16, 5436, 6238
Offset: 1

Views

Author

Rick L. Shepherd, Apr 22 2006

Keywords

Comments

Six terms found and primes proved by PrimeForm ([N+1, Brillhart-Lehmer-Selfridge]). 3*6238^6238-1 has 23674 digits. No more terms <= 8800.
No more terms <= 25000. - Michael S. Branicky, Oct 13 2024

Crossrefs

Cf. A118306, A110931.

Programs

Showing 1-7 of 7 results.

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