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%I #14 Jul 02 2017 12:55:24
%S 3,11,83,6563,43046747,1853020188851911,
%T 3433683820292512484657849089373,
%U 11790184577738583171520872861412518665678211592275841109097151,139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436309
%N Primes of the form 3^(2^n)+k with least nonnegative k.
%C The associated k's are A157979.
%H Florentin Smarandache, <a href="http://arxiv.org/abs/0903.1380">Seven Conjectures in Geometry and Number Theory</a>, Mar 8, 2009.
%F a(n) = 3^(2^n)+k where k = Min{k=>0 such that 3^(2^n)+k is prime} = 3^(2^n)+k where k = Min{k=>0 such that A000244(A000079(n))+k is in A000040}.
%F a(n) = 3^(2^n) + A157979(n).
%e a(0) = 3 because 3^2^0 + 0 = 3^1 + 0 = 3 is prime. a(1) = 11 because 3^2^1 + 2 = 3^2 + 0 = 11 is prime. a(2) = 83 because 3^4 + 2 = 83 is prime. a(3) = 6563 because 3^8 + 2 = 6563 is prime. a(4) = 43046747 because 3^16 + 26 = 43046747 is prime. a(5) = 1853020188851911 because 3^32 + 70 = 1853020188851911 is prime. a(6) = 3433683820292512484657849089373 because 3^64 + 92 = 3433683820292512484657849089373 is prime.
%o (PARI) { a(n) = nextprime( 3^(2^n) ) } \\ _Max Alekseyev_, Sep 13 2009
%Y Cf. A000040, A000079, A000244, A000215, A157979.
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, Mar 10 2009
%E More terms from _Max Alekseyev_, Sep 13 2009
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