A100339 Primes of the form 2^q + q where q is not a prime.

3, 521, 32783, 549755813927, 37778931862957161709643, 2417851639229258349412433

Offset: 1

Author

Cino Hilliard, Jan 11 2005

Keywords

• nonn

Comments

The next term is 2^735+735 = 18073..35103, 222 digits long.

Examples

			For q = 9, 2^9+9 = 521 which is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..11 (terms 1..7 from N. J. A. Sloane)

Crossrefs

Cf. A006127, A057664, A081296, A100556, A129962.

Programs

Mathematica

Select[Table[If[!PrimeQ[n],2^n+n,0],{n,1200}],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011*)

PARI

g1(p,n)=for(x=1,n,c=composite(x);y=p^c+c;if(gcd(y,c)==1,if(isprime(y),print1 (y",")))) composite(n) = \ the n-th composite number { local(c,x); c=1; x=0; while(c <= n, x++; if(!isprime(x),c++); ); return(x) }

Formula

a(n) = A006127(A100556(n-1)) for n >= 2. - Amiram Eldar, Jun 30 2024