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 1-8 of 8 results.

A100360 Duplicate of A061421.

Original entry on oeis.org

2, 7, 71, 110427941548649020598956093796432407239217743554726184882600387580788973
Offset: 1

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Author

Keywords

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

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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

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

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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.

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

A182327 Primes of the form 3^k + k + 1.

Original entry on oeis.org

2, 5, 31, 14348923, 2954312706550833698689, 66555937033867822607895549241096482953017615834735226281, 7282483350946404208076885500996745047522350034970917293604274649554310785227
Offset: 1

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Author

Alex Ratushnyak, Apr 25 2012

Keywords

Crossrefs

Programs

  • Mathematica
    Select[Table[3^n + n + 1, {n, 0, 150}], PrimeQ] (* T. D. Noe, Apr 25 2012 *)

Extensions

a(7) from Seiichi Manyama, Mar 25 2018

A176072 Primes of the form 3^k + 2^k + k + 1.

Original entry on oeis.org

7, 281, 1602529
Offset: 1

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Author

Keywords

Comments

The next term is too large to include here.
281 = 3^5 + 2^5 + 5 + 1,..
The corresponding values of k are 1, 5, 13, 905, 5341, ... ; a(5) ~ 2.016...*10^2548. - Amiram Eldar, Jul 18 2019

Crossrefs

Programs

  • Mathematica
    Select[Array[3^#+2^#+#+1&,2*6! ],PrimeQ[ # ]&]

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

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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

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).

A301637 Primes of the form 4^k + k + 1.

Original entry on oeis.org

2, 19, 5444517870735015415413993718908291383363
Offset: 1

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Author

Seiichi Manyama, Mar 25 2018

Keywords

Crossrefs

Primes of the form b^k+k+1: A061421 (b=2), A182327 (b=3), this sequence (b=4).
Cf. A301633.

Programs

  • Maple
    a:=n->`if`(isprime(4^k+k+1),4^k+k+1,NULL): seq(a(k),k=0..300); # Muniru A Asiru, Mar 25 2018

Formula

a(n) = 4^(2*A301633(n)) + 2*A301633(n) + 1.

A176071 Numbers of the form 2^k + k + 1 that are the product of two distinct primes.

Original entry on oeis.org

21, 38, 265, 4109, 65553, 262163, 1048597, 67108891, 274877906983, 4503599627370549, 73786976294838206531, 75557863725914323419213, 302231454903657293676623, 5192296858534827628530496329220209, 10889035741470030830827987437816582766726, 95780971304118053647396689196894323976171195136475313
Offset: 1

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Author

Keywords

Examples

			21 = 3 * 7 = 2^4 + 4 + 1
		

Crossrefs

Programs

  • Mathematica
    f[n_]:=Last/@FactorInteger[n]=={1,1};Select[Array[2^#+#+1&,140,0],f[ # ]&]
    Select[Table[2^k+k+1,{k,0,200}],PrimeNu[#]==PrimeOmega[#]==2&] (* Harvey P. Dale, Jul 11 2023 *)
  • PARI
    is(n) = my(f = factor(n), e = logint(n, 2)); f[,2] == [1, 1]~ && n == 1<David A. Corneth, May 27 2023

Extensions

Name corrected by David A. Corneth, May 27 2023
Showing 1-8 of 8 results.