A234346 Primes of the form 3^k + 3^m - 1, where k and m are positive integers.

5, 11, 17, 29, 53, 83, 89, 107, 251, 269, 809, 971, 2213, 2267, 4373, 6563, 6569, 6803, 8747, 13121, 19709, 19763, 20411, 59051, 65609, 177173, 183707, 531521, 538001, 590489, 1062881, 1594331, 1594403, 1595051, 1596509, 4782971, 4782977, 4783697, 14348909

Offset: 1

Author

Zhi-Wei Sun, Dec 23 2013

Keywords

• nonn

Comments

Clearly, all terms are congruent to 5 modulo 6.

By a conjecture in A234337 or A234347, this sequence should have infinitely many terms.

Conjecture: For any integer a > 1, there are infinitely many primes of the form a^k + a^m - 1, where k and m are positive integers.

Examples

			a(1) = 5 since 3^1 + 3^1 - 1 = 5 is prime.
a(2) = 11 since 3^2 + 3^1 - 1 = 11 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000079, A000244, A234309, A234310, A234337, A234344, A234347

Programs

Mathematica

n=0;Do[If[PrimeQ[3^k+3^m-1],n=n+1;Print[n," ",3^k+3^m-1]],{m,1,310},{k,1,m}]