A129962 Primes of the form 2^k + k.

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

Offset

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

(PARI) f(n) = forstep(x=1, n, 2, y=2^x+x; if(isprime(y), print1(y", ")))
(Magma) [a: n in [0..400] | IsPrime(a) where a is 2^n + n]; // Vincenzo Librandi, Jul 25 2019

Crossrefs

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

Sequence in context: A183511 A307800 A265796 * A026361 A006189 A092201

Adjacent sequences: A129959 A129960 A129961 * A129963 A129964 A129965

Keyword

nonn

Author

Cino Hilliard, Jun 10 2007

Status

approved