

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
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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

ZhiWei 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^m1], n=n+1; Print[n, " ", 3^k+3^m1]], {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

ZhiWei Sun, Dec 23 2013


STATUS

approved



