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

5, 11, 17, 23, 47, 53, 71, 107, 191, 383, 431, 647, 863, 971, 1151, 2591, 4373, 6143, 6911, 8747, 13121, 15551, 23327, 27647, 62207, 73727, 139967, 165887, 294911, 314927, 442367, 472391, 497663, 786431, 995327, 1062881, 2519423, 10616831, 17915903, 18874367

Offset: 1

Author

Muniru A Asiru, Oct 15 2017

Keywords

• nonn

Comments

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

Examples

			a(1) = 5 = 2^1 * 3^1 - 1.
a(2) = 11 = 2^2 * 3^1 - 1.
a(3) = 17 = 2^1 * 3^2 - 1.
a(4) = 23 = 2^3 * 3^1 - 1.
a(5) = 47 = 2^4 * 3^1 - 1.
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), ...
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..7151 (terms < 10^1000)

Crossrefs

Cf. A000040, A000668, A005105.

Programs

GAP

K:=10^7+1;; # to get all terms <= K.
A:=Filtered([1..K],IsPrime);;
A268640:=List(Positions(List(A,i->Elements(Factors(i+1))),[2,3]),i->A[i]);

Maple

N:= 10^10: # to get all terms <= N
R:= {}:
for b from 1 to floor(log[3]((N+1)/2)) do
     R:= R union select(isprime, {seq(2^a*3^b-1,
          a=1..ilog2((N+1)/3^b))})
od:
sort(convert(R,list)); # Robert Israel, Oct 15 2017

Formula

{ A005105 } \ { 2 } \ { A000668 }.