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A268640 Primes of the form 2^i * 3^j  - 1 for positive i, j. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A214912 A216551 A314255

Adjacent sequences:  A268637 A268638 A268639 * A268641 A268642 A268643

KEYWORD

nonn

AUTHOR

Muniru A Asiru, Oct 15 2017

STATUS

approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)