cp's OEIS Frontend

A277967 Number of even numbers b with 0 < b < 2^n such that b^(2^n) + 1 is prime.

%I A277967 #20 Oct 13 2019 02:32:08
%S A277967 0,1,2,1,1,0,1,0,1,1,1,1,0,0,0,1,2,3,4,1
%N A277967 Number of even numbers b with 0 < b < 2^n such that b^(2^n) + 1 is prime.
%C A277967 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).
%C A277967 Perfect squares b are allowed.
%C A277967 a(20) was determined after a lengthy computation by distributed project PrimeGrid, cf. A321323. - _Jeppe Stig Nielsen_, Jan 02 2019
%H A277967 Y. Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/results.html">Status of the smallest base values yielding Generalized Fermat primes</a>.
%H A277967 PrimeGrid, <a href="http://www.primegrid.com/gfn_history.php">GFN Prime Search Status and History</a>.
%e A277967 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.
%e A277967 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.
%t A277967 Table[Count[Range[2, 2^n - 1, 2], b_ /; PrimeQ[b^(2^n) + 1]], {n, 9}] (* _Michael De Vlieger_, Nov 10 2016 *)
%o A277967 (PARI) a(n)=sum(k=1,2^(n-1)-1,ispseudoprime((2*k)^2^n+1)) \\ slow, only probabilistic primality test
%Y A277967 Cf. A056993, A121270, A259835, A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A057002, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A243959, A321323, etc.
%K A277967 nonn,hard,more
%O A277967 1,3
%A A277967 _Jeppe Stig Nielsen_, Nov 06 2016
%E A277967 a(20) from _Jeppe Stig Nielsen_, Jan 02 2019