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%I #11 Dec 15 2017 17:36:56
%S 2,14,16,18,26,30,36,42,62,132,242,294,302,666,816,824,998,1218,1472,
%T 2522,3098,4148,6404,8102,25656,26490,56702,76442
%N Numbers n such that 65537 * 2^n - 1 is prime.
%C Note that 65537 = 2^16 + 1 is the largest known Fermat prime. All terms have been proved prime. Proof for the largest: PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 65537*2^76442-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 99.98% 65537*2^76442-1 is prime! (101.6260s+0.0044s)
%C No more terms up to 92000.
%t Select[Range[1, 1000], PrimeQ[65537*2^# - 1] &] (* _Julien Kluge_, Jul 08 2016 *)
%o (PARI) is(n)=ispseudoprime(65537*2^n-1) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A112245.
%K more,nonn
%O 1,1
%A _Jason Earls_, Sep 01 2005