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 1-5 of 5 results.

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

Links

Crossrefs

Cf. A001580, A069539, A052007, A048744, A100357, A100358, A100359.
Cf. A061422.

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

Cf. A001580, A052007, A048744, A100357-A100359, A061421.

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

A061422 Numbers k such that 2^(k-1) + k is prime.

Original entry on oeis.org

1, 3, 7, 237, 1885, 51381, 75765
Offset: 1

Views

Author

Jason Earls, May 02 2001

Keywords

Comments

No other terms below 300000. - Giovanni Resta, Nov 12 2012
a(8) > 500000. - Robert Price, May 24 2014

References

  • J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 237, p. 66, Ellipses, Paris 2008.

Links

Crossrefs

Cf. A061421.
Equals A100359(n) + 1.

Programs

Extensions

H. Zeisel found the probable prime 1885. - Benoit Cloitre, Jun 03 2002
New term 51381 from Nuutti Kuosa (see MathPages link). - Max Alekseyev, Feb 08 2009
Deleted an incorrect conjecture. - N. J. A. Sloane, Dec 27 2009
a(7) from Giovanni Resta, Nov 12 2012

A268211 Numbers n of the form 2^k + 1 such that n + k is a prime q (for k >= 0).

Original entry on oeis.org

2, 5, 65, 110427941548649020598956093796432407239217743554726184882600387580788737
Offset: 1

Views

Author

Jaroslav Krizek, Jan 28 2016

Keywords

Comments

Subsequence of A000051.
Corresponding values of numbers k are in A100359 (numbers n such that 2^n+n+1 is prime).
Corresponding values of primes q are in A061421 (primes of the form 2^n+n+1).

Examples

			65 = 2^6 + 1 is a term because 65 + 6 = 71 (prime).

Crossrefs

Cf. A061421, A100359, A268209.

Programs

  • Magma
    [2^n + 1: n in [0..600] | IsPrime(2^n + n + 1)]
  • Mathematica
    2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# + # + 1] &] (* Michael De Vlieger, Jan 29 2016 *)

Formula

a(n) = A061421(n) - A100359(n).

A301744 Numbers k such that 2^k - 2*k + 1 is prime.

Original entry on oeis.org

0, 3, 5, 6, 8, 11, 12, 13, 18, 25, 31, 35, 114, 152, 186, 228, 245, 308, 360, 371, 575, 685, 721, 732, 1361, 2394, 3138, 3446, 5964, 9482, 22793, 51233, 112800, 120491, 199615, 416641
Offset: 1

Views

Author

Vaclav Kotesovec, Mar 26 2018

Keywords

Comments

Terms through 1361 correspond to provable primes; terms beyond 1361 correspond to probable primes.
After 22793, there are no more terms through 40000. - Jon E. Schoenfield, Mar 27 2018
a(37) > 5*10^5. - Robert Price, Jun 01 2018

Crossrefs

Cf. A100359, A100361, A301634.

Programs

  • Magma
    [n: n in [0..1000] |IsPrime(2^n-2*n+1)]; // Vincenzo Librandi, Mar 27 2018
  • Maple
    select(k->isprime(2^k-2*k+1),[$0..3000]); # Muniru A Asiru, Apr 03 2018
  • Mathematica
    Select[Range[0, 1000], PrimeQ[2^# - 2*# + 1] &]
  • PARI
    isok(n) = isprime(2^n-2*n+1); \\ Michel Marcus, Mar 27 2018

Extensions

a(31) from Jon E. Schoenfield, Mar 27 2018
a(32)-a(34) from Robert Price, Apr 03 2018
a(35)-a(36) from Robert Price, Jun 01 2018
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.