A157980 Primes of the form 3^(2^n)+k with least nonnegative k.

3, 11, 83, 6563, 43046747, 1853020188851911, 3433683820292512484657849089373, 11790184577738583171520872861412518665678211592275841109097151, 139008452377144732764939786789661303114218850808529137991604824430036072629766435941001769154109609521811665540548899436309

Offset

0,1

Comments

The associated k's are A157979.

Links

Table of n, a(n) for n=0..8.

Florentin Smarandache, Seven Conjectures in Geometry and Number Theory, Mar 8, 2009.

Formula

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}.

a(n) = 3^(2^n) + A157979(n).

Example

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.

Prog

(PARI) { a(n) = nextprime( 3^(2^n) ) } \\ Max Alekseyev, Sep 13 2009

Crossrefs

Cf. A000040, A000079, A000244, A000215, A157979.

Sequence in context: A335968 A097495 A228034 * A092148 A297485 A231066

Adjacent sequences: A157977 A157978 A157979 * A157981 A157982 A157983

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 10 2009

Extensions

More terms from Max Alekseyev, Sep 13 2009

Status

approved