A100556 Composite numbers q such that 2^q + q is prime.

9, 15, 39, 75, 81, 735, 1311, 1881, 3201, 3225, 11795, 88071, 204129, 678561

Offset: 1

Author

Cino Hilliard, Jan 12 2005

Keywords

• nonn
• more

Examples

			For q = 9, 2^9 + 9 = 521, prime.
Note that 2^11795 + 11795 is prime but 11795 is composite and not divisible by 3.
		

Links

• Cino Hilliard, Title?. [Dead link]

Crossrefs

Composite terms in A052007.

Programs

Mathematica

Do[If[ !PrimeQ[n] && PrimeQ[2^n + n], Print[n]], {n, 2, 10^6}] (* Ryan Propper, Jul 21 2006 *)
nn=15000;Select[Complement[Range[2,nn],Prime[Range[PrimePi[nn]]]], PrimeQ[2^#+#]&] (* Harvey P. Dale, May 05 2011 *)

PARI

\ p^q + q is prime q not prime ptoqpq(p,n)= { local(x,y,q); for(q=6,n, if(q%2, if(!isprime(q), y=p^q+q; if(ispseudoprime(y),print(q","y",")) ) ) ) }

Extensions

a(11) from Ryan Propper, Jul 21 2006

a(12)-a(14) (using A052007) from Michael S. Branicky, Apr 30 2023