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A173053 Numbers n such that 2^(2*n)+2*n+1 is a prime. 2
0, 1, 3, 118, 942, 25690, 37882 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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.)
LINKS
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
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

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Last modified May 20 19:00 EDT 2024. Contains 372720 sequences. (Running on oeis4.)