

A173053


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


2




OFFSET

1,3


COMMENTS

Studying primes of the form 2^(x1)+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.)


LINKS

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


FORMULA

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


MATHEMATICA

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


CROSSREFS

Cf. A061422.
Sequence in context: A155209 A037117 A283883 * A180393 A172013 A143781
Adjacent sequences: A173050 A173051 A173052 * A173054 A173055 A173056


KEYWORD

nonn,more


AUTHOR

Vincenzo Librandi, Feb 08 2010


EXTENSIONS

Display of very long primes truncated by R. J. Mathar, Feb 15 2010
a(7) from Vincenzo Librandi, Jun 07 2014


STATUS

approved



