|
%I #10 Dec 24 2013 01:45:42
%S 5,11,17,29,53,83,89,107,251,269,809,971,2213,2267,4373,6563,6569,
%T 6803,8747,13121,19709,19763,20411,59051,65609,177173,183707,531521,
%U 538001,590489,1062881,1594331,1594403,1595051,1596509,4782971,4782977,4783697,14348909
%N Primes of the form 3^k + 3^m - 1, where k and m are positive integers.
%C Clearly, all terms are congruent to 5 modulo 6.
%C By a conjecture in A234337 or A234347, this sequence should have infinitely many terms.
%C 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.
%H Zhi-Wei Sun, <a href="/A234346/b234346.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1) = 5 since 3^1 + 3^1 - 1 = 5 is prime.
%e a(2) = 11 since 3^2 + 3^1 - 1 = 11 is prime.
%t 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}]
%Y Cf. A000040, A000079, A000244, A234309, A234310, A234337, A234344, A234347
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Dec 23 2013
|
