A069353 - OEIS

%I #13 Jul 13 2023 02:02:39

%S 0,1,2,3,5,7,8,11,15,17,23,26,31,35,47,53,63,71,80,95,107,127,143,161,

%T 191,215,242,255,287,323,383,431,485,511,575,647,728,767,863,971,1023,

%U 1151,1295,1457,1535,1727,1943,2047,2186,2303,2591,2915,3071,3455,3887

%N Numbers of form 2^i*3^j - 1 with i, j >= 0.

%C Are there infinitely many primes in this sequence? See A005105.

%C If m is a term then also 2*m + 1 and 3*m + 2.

%H Graham Everest, Peter Rogers, and Thomas Ward, <a href="https://doi.org/10.1007/3-540-45455-1_8">A higher-rank Mersenne problem</a>, Algorithmic Number Theory: 5th International Symposium, ANTS-V Sydney, Australia, July 7-12, 2002 Proceedings 5, Lect. Notes Computer Sci. 2369, Springer Berlin Heidelberg, 2002, pp. 95-107.

%F a(n) = A003586(n)-1.

%t With[{max = 4000}, Sort[Flatten[Table[2^i*3^j - 1, {i, 0, Log2[max]}, {j, 0, Log[3, max/2^i]}]]]] (* _Amiram Eldar_, Jul 13 2023 *)

%Y Cf. A003586, A055600, A069355, A005105.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Mar 18 2002