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.

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

A301644 Primes of form 3*k^k + 1.

Original entry on oeis.org

13, 769, 139969, 30000000001
Offset: 1

Views

Author

Seiichi Manyama, Mar 25 2018

Keywords

Comments

The next term is too large to include.
The next term (a(5)) has 703 digits. - Harvey P. Dale, Sep 04 2018

Crossrefs

Primes of form b*k^k + 1: A121270 (b=1), A216148 (b=2), this sequence (b=3), A301641 (b=4), A301642 (b=16).
Cf. A160600.

Programs

  • Mathematica
    Select[Table[3*k^k+1,{k,500}],PrimeQ] (* Harvey P. Dale, Sep 04 2018 *)

Formula

a(n) = 3*(2*A160600(n))^(2*A160600(n)) + 1.

A301519 Numbers k such that 4*k^k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 7, 25, 7143, 11583
Offset: 1

Views

Author

Seiichi Manyama, Mar 23 2018

Keywords

Comments

a(9) > 20000, if it exists. All terms correspond to certified primes. - Giovanni Resta, Apr 06 2018

Crossrefs

Cf. A110932, A160600, A301520, A301522.

Programs

  • Mathematica
    Flatten[{0, Select[Range[1000], PrimeQ[4*#^# + 1] &]}] (* Vaclav Kotesovec, Mar 25 2018 *)
  • PARI
    for(n=0, 100, if(isprime(4*n^n+1), print1(n", ")))

Extensions

a(7)-a(8) from Giovanni Resta, Apr 06 2018

A301522 Numbers k such that 16*k^k + 1 is prime.

Original entry on oeis.org

0, 1, 3, 6, 12, 60, 85, 87, 612, 9073
Offset: 1

Views

Author

Seiichi Manyama, Mar 23 2018

Keywords

Crossrefs

Cf. A110932, A160600, A301519.

Programs

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

Extensions

a(10) from Michael S. Branicky, Apr 16 2023
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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