%I #16 Jan 16 2024 01:38:10
%S 3,6,9,12,18,24,36,48,72,96,144,192,288,384,576,768,1152,1536,2304,
%T 3072,4608,6144,9216,12288,18432,24576,36864,49152,73728,98304,147456,
%U 196608,294912,393216,589824,786432,1179648,1572864,2359296,3145728,4718592,6291456,9437184,12582912,18874368,25165824,37748736,50331648
%N Numbers of the form 3*2^k or 9*2^k.
%F Sum_{n>=1} 1/a(n) = 8/9. - _Amiram Eldar_, Jan 16 2024
%t seq[max_] := Union[Table[3*2^n, {n, 0, Floor[Log2[max/3]]}], Table[9*2^n, {n, 0, Floor[Log2[max/9]]}]]; seq[10^8] (* _Amiram Eldar_, Jan 16 2024 *)
%Y The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Jul 12 2022