A173053 Numbers n such that 2^(2*n)+2*n+1 is a prime.

0, 1, 3, 118, 942, 25690, 37882

Offset: 1

Author

Vincenzo Librandi, Feb 08 2010

Keywords

• nonn
• more

Comments

Studying primes of the form 2^(x-1)+x for x=2n+1 leads to A061422. The six odd x in A061422 give the known solutions shown here. [R. J. Mathar]

The associated primes are 1+1 = 2, 2^2+3 = 7, 2^6+7 = 71,

2^236+237 = 110427941548649020598956093796432407239217743554726184882600387580788973;

2^1884+1885 = 1382012053...8525348701 (Most inner digits omitted. The number of digits of the prime grows roughly as log_10(4^n) = 0.61*n.)

Crossrefs

Cf. A061422.

Programs

Mathematica

Select[Range[0, 2000], PrimeQ[2^(2 #) + 2 # + 1] &] (* Vincenzo Librandi, Jun 07 2014 *)

Formula

a(n) = floor( A061422(n) / 2). - Michel Marcus, Jun 07 2014

Extensions

Display of very long primes truncated by R. J. Mathar, Feb 15 2010

a(7) from Vincenzo Librandi, Jun 07 2014