OFFSET
1,3
COMMENTS
The choice whether to take b < 2^n or b <= 2^n matters only for n=1 and n=2 unless there are more primes like 2^2+1 and 4^4+1 (see A121270).
Perfect squares b are allowed.
a(20) was determined after a lengthy computation by distributed project PrimeGrid, cf. A321323. - Jeppe Stig Nielsen, Jan 02 2019
LINKS
EXAMPLE
For n=18, we get b^262144 + 1 is prime for b=24518, 40734, 145310, 361658, 525094, ...; the first 3 of these b values are strictly below 262144, hence a(18)=3.
The corresponding primes are 2^4+1; 2^8+1, 4^8+1; 2^16+1; 30^32+1; 120^128+1; 46^512+1; etc.
MATHEMATICA
Table[Count[Range[2, 2^n - 1, 2], b_ /; PrimeQ[b^(2^n) + 1]], {n, 9}] (* Michael De Vlieger, Nov 10 2016 *)
PROG
(PARI) a(n)=sum(k=1, 2^(n-1)-1, ispseudoprime((2*k)^2^n+1)) \\ slow, only probabilistic primality test
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jeppe Stig Nielsen, Nov 06 2016
EXTENSIONS
a(20) from Jeppe Stig Nielsen, Jan 02 2019
STATUS
approved