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 1-10 of 20 results. Next

A216375 Numbers k such that 11^k + k^11 + 1 is prime.

Original entry on oeis.org

0, 1, 5, 941, 23071
Offset: 1

Views

Author

Vincenzo Librandi, Sep 06 2012

Keywords

Comments

a(6) > 10^5. - Robert Price, Jan 16 2013

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 5000], PrimeQ[11^# + #^11 + 1] &]
  • PARI
    is(n)=isprime(11^n+n^11+1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5) from Robert Price, Jan 16 2014

A061421 Primes of the form 2^n+n+1.

Original entry on oeis.org

2, 7, 71, 110427941548649020598956093796432407239217743554726184882600387580788973
Offset: 1

Views

Author

Jason Earls, May 02 2001

Keywords

Comments

Next term is 2^1884+1884+1, with 568 digits and is too large to include. - Emeric Deutsch, May 13 2006
The Wikipedia article "Zeisel number" gives a historical connection to A051015. - Jonathan Sondow, Oct 17 2017

Crossrefs

Programs

  • Maple
    a:=proc(n) if isprime(2^n+n+1)=true then 2^n+n+1 else fi end: seq(a(n),n=0..1000); # Emeric Deutsch, May 13 2006
  • Mathematica
    {ta={{0}}, tb={{0}}};Do[g=n;s=2^n+n+1; If[PrimeQ[s], Print[n];ta=Append[ta, n]; tb=Append[tb, s]], {n, 1, 10000}];{ta, tb, g} (* Labos Elemer, Nov 19 2004 *)

Extensions

Edited by N. J. A. Sloane, May 04 2007

A100361 Numbers k such that 2^k - k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 4, 6, 16, 18, 54, 58, 100, 120, 504, 1302, 3234, 14748, 16102, 22782, 34656, 64764, 70866, 194940, 274074, 313344, 331416, 354640
Offset: 1

Views

Author

Labos Elemer, Nov 19 2004

Keywords

Comments

a(21) > 150000. - Giovanni Resta, Mar 18 2014
a(26) > 5*10^5. - Robert Price, Oct 13 2014

Crossrefs

Programs

  • Maple
    A100361:=n->`if`(isprime(2^n-n+1), n, NULL): seq(A100361(n), n=0..10^3); # Wesley Ivan Hurt, Oct 13 2014
  • Mathematica
    {ta={{0}}, tb={{0}}};Do[g=n;s=2^n-n+1; If[PrimeQ[s], Print[n];ta=Append[ta, n]; tb=Append[tb, s]], {n, 1, 10000}];{ta, tb, g}
  • PARI
    is(n)=ispseudoprime(2^n-n+1) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

a(15)-a(20) from Giovanni Resta, Mar 18 2014
a(21)-a(25) from Robert Price, Oct 13 2014

A100362 Primes of the form 2^k - k + 1.

Original entry on oeis.org

2, 2, 3, 13, 59, 65521, 262127, 18014398509481931, 288230376151711687, 1267650600228229401496703205277, 1329227995784915872903807060280344457
Offset: 1

Views

Author

Labos Elemer, Nov 19 2004

Keywords

Comments

The next term has 151 digits. - Stefan Steinerberger, Feb 11 2006

Crossrefs

Programs

  • Magma
    [ a: n in [0..200] | IsPrime(a) where a is 2^n-n+1 ]; // Vincenzo Librandi, Jul 18 2012
    
  • Mathematica
    Select[Table[2^n-n+1,{n,0,500}],PrimeQ] (* Vincenzo Librandi, Jul 18 2012 *)
  • Sage
    def list_a(k):
      return [(2**i) - i + 1 for i in range(k) if (2**i) - i + 1 in Primes()] # Giuseppe Bonaccorso, Aug 15 2019

A035325 Primes of the form 2^k + k^2 + 1.

Original entry on oeis.org

2, 101, 4241, 262469, 5846006549323611672814739330865132078623730198149, 6277101735386680763835789423207666416102355444464034549761, 105312291668557186697918027683670432318895095400549111254311024193
Offset: 1

Views

Author

Keywords

Comments

Corresponding k's (A100357) all are multiples of 6. - Zak Seidov, Apr 05 2014

Crossrefs

Cf. A100357 (corresponding n's). - Zak Seidov, Apr 05 2014

Programs

  • Magma
    [ a: n in [0..250] | IsPrime(a) where a is 2^n + n^2 + 1 ] // Vincenzo Librandi, Sep 03 2012
  • Mathematica
    Select[Table[2^n + n^2 + 1, {n, 0, 300, 6}], PrimeQ ] (* Vincenzo Librandi, Sep 03 2012 *)

Extensions

More terms from James Sellers

A100359 Numbers k such that 2^k + k + 1 is prime.

Original entry on oeis.org

0, 2, 6, 236, 1884, 51380, 75764
Offset: 1

Views

Author

Labos Elemer, Nov 19 2004

Keywords

Comments

a(8) > 500000. - Robert Price, May 24 2014

Crossrefs

Programs

  • Mathematica
    {ta={{0}}, tb={{0}}};Do[g=n;s=2^n+n+1; If[PrimeQ[s], Print[n];ta=Append[ta, n]; tb=Append[tb, s]], {n, 1, 10000}];{ta, tb, g}
  • PARI
    is(n)=ispseudoprime(2^n+n+1) \\ Charles R Greathouse IV, Feb 20 2017

Formula

a(n) = A061422(n) - 1.

Extensions

a(6) from A061422 Max Alekseyev, Feb 08 2009
a(7) from Giovanni Resta, Mar 19 2014

A100358 Numbers n such that 2^n+n^3+1 is prime.

Original entry on oeis.org

0, 2, 6, 8, 20, 38, 96, 146, 236, 458, 726, 962, 1422, 2864, 3858, 5228, 9822, 21774, 32336, 33336, 43556
Offset: 1

Views

Author

Labos Elemer, Nov 19 2004

Keywords

Comments

a(22) > 200000. - Giovanni Resta, Mar 23 2014
a(22) > 400000. - Robert Price, Sep 01 2014

Crossrefs

Programs

  • Maple
    A100358:=n->`if`(isprime(2^n+n^3+1),n,NULL): seq(A100358(n), n=0..10^3); # Wesley Ivan Hurt, Sep 01 2014
  • Mathematica
    {ta={{0}}, tb={{0}}}; Do[g=n;s=2^n+n^3+1;If[PrimeQ[s], Print[n];ta=Append[ta, n];tb=Append[tb, s]], {n, 1, 10000}];{ta, tb, g}
  • PARI
    for(n=1,10^5,if(ispseudoprime(2^n+n^3+1),print1(n,", "))) \\ Derek Orr, Sep 01 2014

Extensions

a(17)-a(21) from Giovanni Resta, Mar 23 2014

A215444 Numbers k such that 7^k + k^7 + 1 is prime.

Original entry on oeis.org

0, 3, 5, 15, 375, 98003
Offset: 1

Views

Author

Vincenzo Librandi, Sep 06 2012

Keywords

Comments

a(6) > 8000. - Joerg Arndt, Sep 29 2012
a(7) > 2*10^5. - Robert Price, Jun 15 2014

Crossrefs

Programs

  • Magma
    [k: k in [0..400] | IsPrime(7^k + k^7 + 1)];
    
  • Mathematica
    Select[Range[0, 5000], PrimeQ[7^# + #^7 + 1] &]
  • PARI
    is(n)=ispseudoprime(7^n+n^7+1) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

a(6) from Robert Price, May 24 2014

A215445 Numbers k such that 7^k + k^7 - 1 is prime.

Original entry on oeis.org

1, 11, 65, 133, 679, 1571, 27517, 51631
Offset: 1

Views

Author

Vincenzo Librandi, Sep 06 2012

Keywords

Comments

a(9) > 10^5. - Robert Price, Feb 23 2014

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 5000], PrimeQ[7^# + #^7 - 1] &]
  • PARI
    is(n)=ispseudoprime(7^n+n^7-1) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

a(7)-a(8) from Robert Price, Feb 23 2014

A216423 Numbers k such that 4^k + k^4 + 1 is prime.

Original entry on oeis.org

0, 6, 12, 3804, 8346, 15528, 147036
Offset: 1

Views

Author

Vincenzo Librandi, Sep 07 2012

Keywords

Comments

a(8) > 2*10^5. - Robert Price, Apr 29 2014
a(1)-a(3) are trivially prime. a(4)-a(7) are probable primes. - Robert Price, May 07 2014

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 5000], PrimeQ[4^# + #^4 + 1] &]
  • PARI
    is(n)=ispseudoprime(4^n+n^4+1) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

a(5)-a(7) from Robert Price, Apr 29 2014
Showing 1-10 of 20 results. Next