%I
%S 2,5,8179,524269
%N Primes of the form 2^p  p where p is prime.
%C Next term, if it exists, has more than 618 digits.  _Emeric Deutsch_, Mar 27 2005
%C Next term, if it exists, has more than 10,000 digits.
%C The corresponding primes p are: 2, 3, 13, 19, ....  _Gerasimov Sergey_, Jul 26 2013
%C 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
%C Next term is 2^481801481801. 2^4818011 is not a Mersenne prime.  _Joerg Arndt_, Jul 19 2016
%e 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
%p 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_
%t lst={};Do[p=Prime[n];If[PrimeQ[p=2^pp],AppendTo[lst,p]],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 28 2009 *)
%t Select[Table[2^pp,{p,Prime[Range[20]]}],PrimeQ] (* _Harvey P. Dale_, Sep 20 2018 *)
%Y Cf. A000668, A057663, A057664, A057665, A056677.
%K nonn,more
%O 1,1
%A _Labos Elemer_, Oct 19 2000
