A129962 Primes of the form 2^k + k.

3, 11, 37, 521, 32783, 549755813927, 37778931862957161709643, 2417851639229258349412433, 618970019642690137449562201, 266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867389

Offset: 1

Author

Cino Hilliard, Jun 10 2007

Keywords

• nonn

Comments

It is convenient, although not necessary, to let k be an odd number since k even => 2^k + k is even > 2.

Conjecture: sequence is infinite.

If k is prime we have A057664.

Examples

			For k = 3, 2^3 + 3 = 11 prime, so 11 is a term.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..16

Crossrefs

Cf. A052007 (values of k), A057664, A081296.

Programs

Magma

[a: n in [0..400] | IsPrime(a) where a is 2^n + n]; // Vincenzo Librandi, Jul 25 2019

Mathematica

Select[Table[2^n+n,{n,600}],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)

PARI

f(n) = forstep(x=1,n,2,y=2^x+x;if(isprime(y),print1(y",")))