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 1-3 of 3 results.

A057664 Primes of the form p + 2^p where p is prime.

Original entry on oeis.org

11, 37, 618970019642690137449562201, 266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867389
Offset: 1

Views

Author

Labos Elemer, Oct 16 2000

Keywords

Comments

The next term has 212 digits. - Harvey P. Dale, Feb 19 2018

Crossrefs

Programs

A057678 Primes of the form 2^p - p where p is prime.

Original entry on oeis.org

2, 5, 8179, 524269
Offset: 1

Views

Author

Labos Elemer, Oct 19 2000

Keywords

Comments

Next term, if it exists, has more than 618 digits. - Emeric Deutsch, Mar 27 2005
Next term, if it exists, has more than 10,000 digits.
The corresponding primes p are: 2, 3, 13, 19, .... - Gerasimov Sergey, Jul 26 2013
The corresponding 2^p - 1 are 3, 7, 8191, 524287 which are Mersenne primes (A000668). Is this the case for all members of the sequence? None of the other Mersenne primes < 2^132049-1 correspond to members of the sequence. - Robert Israel, Jul 18 2016
Next term is 2^481801-481801. 2^481801-1 is not a Mersenne prime. - Joerg Arndt, Jul 19 2016

Examples

			p=3 is prime, and so is 2^p - p = 8 - 3 = 5, so 5 is in the sequence. - _Michael B. Porter_, Jul 19 2016
		

Crossrefs

Programs

  • Maple
    a:=proc(n) if isprime(2^ithprime(n)-ithprime(n))=true then 2^ithprime(n)-ithprime(n) else fi end: seq(a(n),n=1..310); # Emeric Deutsch
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p=2^p-p],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
    Select[Table[2^p-p,{p,Prime[Range[20]]}],PrimeQ] (* Harvey P. Dale, Sep 20 2018 *)

A057663 Primes p such that p + 2^p is also a prime.

Original entry on oeis.org

3, 5, 89, 317, 701
Offset: 1

Views

Author

Labos Elemer, Oct 16 2000

Keywords

Comments

Different from A056206, where, e.g., at n=89, 89 is not minimal, A056206(89)=29 and not 89.
a(6) > 27479. - Ralf Stephan, Oct 23 2002
Intersection of A000040 and A052007. - Iain Fox, Nov 08 2017
a(6) > 678561. - Iain Fox, Nov 08 2017
Every term other than 3 is congruent to 5 (mod 6). - Arkadiusz Wesolowski, Nov 14 2017
These terms satisfy phi(k + 2^k) = phi(k) + 2^k, where phi is A000010, the Euler totient function. Conjecture: this sequence gives all numbers k that satisfy the condition phi(k + 2^k) = phi(k) + 2^k. - Juri-Stepan Gerasimov, May 23 2019

Examples

			q=3, 2^3 + 3 = 11 a prime.
		

Crossrefs

Programs

  • Magma
    [p: p in PrimesUpTo(1000) | IsPrime(2^p+p) ] // Vincenzo Librandi, Aug 07 2010
    
  • Mathematica
    Select[Prime@ Range[10^3], PrimeQ[# + 2^#] &] (* Michael De Vlieger, Nov 08 2017 *)
  • PARI
    lista(nn) = forprime(p=3, nn, if(ispseudoprime(p + 2^p), print1(p, ", "))) \\ Iain Fox, Nov 13 2017
    
  • Sage
    [n for n in (1..1000) if is_prime(n) and is_prime(2^n+n)] # G. C. Greubel, May 24 2019
Showing 1-3 of 3 results.