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Primes of the form 2^i * 3^j - 1 for positive i, j.
1

%I #38 Sep 17 2019 11:39:21

%S 5,11,17,23,47,53,71,107,191,383,431,647,863,971,1151,2591,4373,6143,

%T 6911,8747,13121,15551,23327,27647,62207,73727,139967,165887,294911,

%U 314927,442367,472391,497663,786431,995327,1062881,2519423,10616831,17915903,18874367

%N Primes of the form 2^i * 3^j - 1 for positive i, j.

%C a(n) is congruent to 5 (mod 6).

%H Ray Chandler, <a href="/A268640/b268640.txt">Table of n, a(n) for n = 1..7151</a> (terms < 10^1000)

%F { A005105 } \ { 2 } \ { A000668 }.

%e a(1) = 5 = 2^1 * 3^1 - 1.

%e a(2) = 11 = 2^2 * 3^1 - 1.

%e a(3) = 17 = 2^1 * 3^2 - 1.

%e a(4) = 23 = 2^3 * 3^1 - 1.

%e a(5) = 47 = 2^4 * 3^1 - 1.

%e List of (i, j): (1, 1), (2, 1), (1, 2), (3, 1), (4, 1), (1, 3), (3, 2), (2, 3), (6, 1), (7, 1), (4, 3), (3, 4), (5, 3), (2, 5), (7, 2), (5, 4), ...

%p N:= 10^10: # to get all terms <= N

%p R:= {}:

%p for b from 1 to floor(log[3]((N+1)/2)) do

%p R:= R union select(isprime, {seq(2^a*3^b-1,

%p a=1..ilog2((N+1)/3^b))})

%p od:

%p sort(convert(R,list)); # _Robert Israel_, Oct 15 2017

%o (GAP) K:=10^7+1;; # to get all terms <= K.

%o A:=Filtered([1..K],IsPrime);;

%o A268640:=List(Positions(List(A,i->Elements(Factors(i+1))),[2,3]),i->A[i]);

%Y Cf. A000040, A000668, A005105.

%K nonn

%O 1,1

%A _Muniru A Asiru_, Oct 15 2017