A129963 Primes of the form 4^k + k.

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..7.

Example

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A197776 A197606 A207979 * A115764 A252794 A328359

Adjacent sequences: A129960 A129961 A129962 * A129964 A129965 A129966

Keyword

nonn

Author

Cino Hilliard, Jun 10 2007, Aug 20 2007

Status

approved