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

1,1

Comments

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

Links

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

Formula

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

Example

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), ...

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

Prog

(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]);

Crossrefs

Cf. A000040, A000668, A005105.

Sequence in context: A147305 A049755 A096449 * A360542 A214912 A216551

Adjacent sequences: A268637 A268638 A268639 * A268641 A268642 A268643

Keyword

nonn

Author

Muniru A Asiru, Oct 15 2017

Status

approved