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

1,1

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.

Links

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

Example

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

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}]

Crossrefs

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

Sequence in context: A046135 A331946 A162336 * A074267 A268518 A268521

Adjacent sequences: A234343 A234344 A234345 * A234347 A234348 A234349

Keyword

nonn

Author

Zhi-Wei Sun, Dec 23 2013

Status

approved