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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

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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))}: