cp's OEIS Frontend

A268640 Primes of the form 2^i * 3^j - 1 for positive i, j.

%I A268640 #38 Sep 17 2019 11:39:21
%S A268640 5,11,17,23,47,53,71,107,191,383,431,647,863,971,1151,2591,4373,6143,
%T A268640 6911,8747,13121,15551,23327,27647,62207,73727,139967,165887,294911,
%U A268640 314927,442367,472391,497663,786431,995327,1062881,2519423,10616831,17915903,18874367
%N A268640 Primes of the form 2^i * 3^j  - 1 for positive i, j.
%C A268640 a(n) is congruent to 5 (mod 6).
%H A268640 Ray Chandler, <a href="/A268640/b268640.txt">Table of n, a(n) for n = 1..7151</a> (terms < 10^1000)
%F A268640 { A005105 } \ { 2 } \ { A000668 }.
%e A268640 a(1) = 5 = 2^1 * 3^1 - 1.
%e A268640 a(2) = 11 = 2^2 * 3^1 - 1.
%e A268640 a(3) = 17 = 2^1 * 3^2 - 1.
%e A268640 a(4) = 23 = 2^3 * 3^1 - 1.
%e A268640 a(5) = 47 = 2^4 * 3^1 - 1.
%e A268640 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 A268640 N:= 10^10: # to get all terms <= N
%p A268640 R:= {}:
%p A268640 for b from 1 to floor(log[3]((N+1)/2)) do
%p A268640      R:= R union select(isprime, {seq(2^a*3^b-1,
%p A268640           a=1..ilog2((N+1)/3^b))})
%p A268640 od:
%p A268640 sort(convert(R,list)); # _Robert Israel_, Oct 15 2017
%o A268640 (GAP)  K:=10^7+1;; # to get all terms <= K.
%o A268640 A:=Filtered([1..K],IsPrime);;
%o A268640 A268640:=List(Positions(List(A,i->Elements(Factors(i+1))),[2,3]),i->A[i]);
%Y A268640 Cf. A000040, A000668, A005105.
%K A268640 nonn
%O A268640 1,1
%A A268640 _Muniru A Asiru_, Oct 15 2017