

A057678


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


6




OFFSET

1,1


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 < 2^1320491 correspond to members of the sequence.  Robert Israel, Jul 18 2016
Next term is 2^481801481801. 2^4818011 is not a Mersenne prime.  Joerg Arndt, Jul 19 2016


LINKS

Table of n, a(n) for n=1..4.


EXAMPLE

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


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^pp], AppendTo[lst, p]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
Select[Table[2^pp, {p, Prime[Range[20]]}], PrimeQ] (* Harvey P. Dale, Sep 20 2018 *)


CROSSREFS

Cf. A000668, A057663, A057664, A057665, A056677.
Sequence in context: A187604 A082815 A115893 * A090071 A247148 A139062
Adjacent sequences: A057675 A057676 A057677 * A057679 A057680 A057681


KEYWORD

nonn,more


AUTHOR

Labos Elemer, Oct 19 2000


STATUS

approved



