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.

A100357 Numbers k such that 2^k + k^2 + 1 is prime.

Original entry on oeis.org

0, 6, 12, 18, 162, 192, 216, 420, 1524, 5112, 7404, 24216, 25944, 101832, 346854
Offset: 1

Views

Author

Labos Elemer, Nov 19 2004

Keywords

Comments

a(15) > 200000. - Giovanni Resta, Mar 23 2014
All terms are multiples of 6. Corresponding primes of the form 2^n+n^2+1 are in A035325. - Zak Seidov, Apr 05 2014
a(16) > 5*10^5. - Robert Price, Jun 15 2014

Crossrefs

Programs

  • Magma
    [n: n in [0..800] | IsPrime(2^n + n^2 + 1) ]; // Vincenzo Librandi, Sep 03 2012
    
  • Mathematica
    {ta={{0}}, tb={{0}}}; Do[g=n;s=2^n+n^2+1;If[PrimeQ[s], Print[n];ta=Append[ta, n];tb=Append[tb, s]], {n, 0, 10000, 6}];{ta, tb, g}
    Select[Range[0, 10000, 6], PrimeQ[2^# + #^2 + 1] &] (* Vincenzo Librandi, Sep 03 2012 *)
  • PARI
    is(n)=isprime(2^n+n^2+1) \\ Charles R Greathouse IV, Jul 01 2013

Extensions

Added a(1) from Vincenzo Librandi, Sep 03 2012
a(12)-a(14) from Giovanni Resta, Mar 23 2014
Mathematica codes edited by Zak Seidov, Apr 05 2014
a(15) from Robert Price, Jun 15 2014

A215434 Primes of form 2^k + k^2 - 1.

Original entry on oeis.org

2, 7, 31, 1123, 1180591620717411308323, 21778071482940061661655974875633165551139, 89202980794122492566142873090593446023942979, 1569275433846670190958947355801916604025588861116008664323
Offset: 1

Views

Author

Vincenzo Librandi, Sep 03 2012

Keywords

Crossrefs

Programs

  • Magma
    [a: n in [0..250] | IsPrime(a) where a is 2^n+n^2-1];
  • Mathematica
    Select[Table[2^n + n^2 - 1, {n, 0, 300}], PrimeQ]

A182357 Primes of the form 2^n + n^2 + 2.

Original entry on oeis.org

3, 5, 19, 59, 179, 8363, 131363, 134218459, 2147484611, 49039857307708443467467104868809893875799651909875303859, 3291009114642412084309938365114701009965471731267159726697262571
Offset: 1

Views

Author

Alex Ratushnyak, Apr 26 2012

Keywords

Crossrefs

Programs

  • Mathematica
    Select[Table[2^n+n^2+2,{n,1000}],PrimeQ] (* Harvey P. Dale, Jul 22 2012 *)

Extensions

More terms (a(10) and a(11)) from Harvey P. Dale, Jul 22 2012

A216592 Numbers m such that 8^m + m^8 + 1 is prime.

Original entry on oeis.org

0, 108, 27018
Offset: 1

Views

Author

Vincenzo Librandi, Sep 09 2012

Keywords

Comments

Next term > 2*10^4.
a(4) > 10^5. - Robert Price, Oct 08 2015

Examples

			8^0 + 0^8 + 1 = 2, which is prime, so 0 is in the sequence.
		

Crossrefs

Cf. Numbers m such that k^m + m^k + 1 is prime: A100357 (k=2), A215441 (k=3), A216423 (k=4), A215442 (k=5), A243934 (k=6), A215444 (k=7), this sequence (k=8), A216618 (k=10), A216375 (k=11), A216421 (k=13).
Cf. Numbers m such that k^m + m^k - 1 is prime: A215439 (k=2), A215440 (k=3), A216424 (k=4), A215443 (k=5), A216425 (k=6), A215445 (k=7), A216591 (k=8), A216619 (k=10), A215446 (k=11), A216420 (k=13), A216422 (k=19).
Cf. Primes of form k^m + m^k + 1: A035325 (k=2), A215436 (k=3), A215438 (k=5).
Cf. Primes of form k^m + m^k - 1: A215434 (k=2), A215435 (k=3), A215437 (k=5).

Programs

  • Mathematica
    Select[Range[0, 10000], PrimeQ[8^# + #^8 + 1] &]
  • PARI
    is(n)=ispseudoprime(8^n+n^8+1) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(3) from Robert Price, Oct 08 2015
Showing 1-4 of 4 results.