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A057678 Primes of the form 2^p - p where p is prime. 6

%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 < 2^132049-1 correspond to members of the sequence. - _Robert Israel_, Jul 18 2016

%C Next term is 2^481801-481801. 2^481801-1 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^p-p],AppendTo[lst,p]],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 28 2009 *)

%t Select[Table[2^p-p,{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

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)