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A057678 Primes of the form 2^p - p where p is prime. 7
2, 5, 8179, 524269 (list; graph; refs; listen; history; text; internal format)
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 < 2^132049-1 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
LINKS
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^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 *)
CROSSREFS
Sequence in context: A082815 A115893 A323338 * A090071 A319898 A325957
KEYWORD
nonn,more
AUTHOR
Labos Elemer, Oct 19 2000
STATUS
approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)