A157980 - OEIS

%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