A129963 Primes of the form 4^k + k.

5, 67, 262153, 1073741839, 18889465931478580854821, 1496577676626844588240573268701473812127674924007509, 118571099379011784113736688648896417641748464297615937576404566024103044751294597

Offset: 1

Author

Cino Hilliard, Jun 10 2007, Aug 20 2007

Keywords

• nonn

Comments

It is convenient, although not necessary, to let k be an odd number since k even => 4^k + k is even > 2.

Conjecture: sequence is infinite.

The next term (a(8)) has 126 digits. - Harvey P. Dale, Jun 05 2014

Examples

			For k = 3, 4^3 + 3 = 67 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..9

Crossrefs

Cf. A057909, A158879.

Programs

Mathematica

Select[Table[4^n+n,{n,1,251,2}],PrimeQ] (* Harvey P. Dale, Jun 05 2014 *)

PARI

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

Formula

a(n) = A158879(A057909(n)). - Amiram Eldar, Jul 04 2024