A349638 Primes of the form (2^a+1)*(3^b+1)-1 with a, b >= 0.

3, 5, 7, 11, 17, 19, 29, 67, 83, 89, 131, 139, 163, 251, 257, 409, 487, 1289, 1459, 4099, 6563, 6569, 10939, 12409, 15859, 32771, 39367, 59051, 65537, 65539, 81929, 94169, 98419, 229403, 262147, 327689, 335953, 748249, 999667, 1279459, 1343569, 1594331, 1948649, 4782971, 4782977, 9034513

Offset

1,1

Comments

It appears that the only term that has more than one such representation is 19 = (2^0+1)*(3^2+1)-1 = (2^2+1)*(3^1+1)-1.

Links

Robert Israel, Table of n, a(n) for n = 1..1635

Example

a(7) = 29 is a term because it is (2^1+1)*(3^2+1)-1 and is prime.

Maple

N:= 10^20: # for all terms <= N
S:= {seq(seq((2^a+1)*(3^b+1)-1, b=0..ilog[3]((N+1)/(2^a+1)-1)), a=0..ilog[2]((N-1)/2))}:
sort(convert(select(isprime, S), list));

Crossrefs

Sequence in context: A155779 A337815 A235476 * A045397 A211409 A152998

Adjacent sequences: A349635 A349636 A349637 * A349639 A349640 A349641

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 31 2021

Status

approved