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A234346
Primes of the form 3^k + 3^m - 1, where k and m are positive integers.
12
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.
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}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Dec 23 2013
STATUS
approved