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Sequence formed as follows: for each k >= 0, insert between 3^k and 3^(k+1) the least power of 2 than is in the interval [3^k, 3^(k+1)], and then arrange the resulting numbers in nondecreasing order.
2

%I #15 May 29 2024 10:21:18

%S 1,1,3,4,9,16,27,32,81,128,243,256,729,1024,2187,4096,6561,8192,19683,

%T 32768,59049,65536,177147,262144,531441,1048576,1594323,2097152,

%U 4782969,8388608,14348907,16777216,43046721,67108864,129140163,134217728,387420489

%N Sequence formed as follows: for each k >= 0, insert between 3^k and 3^(k+1) the least power of 2 than is in the interval [3^k, 3^(k+1)], and then arrange the resulting numbers in nondecreasing order.

%e 3^0 <= 2^0 < 3^1 < 2^2 < 3^2 < 2^4 < 3^3 < ...

%p [seq(op([3^i, 2^ceil(log[2](3^i))]),i=0..50)]; # _Robert Israel_, May 22 2024

%t a[n_] := If[EvenQ[n], 3^(n/2), 2^Ceiling[((n - 1)/2) Log[3]/Log[2]]]

%t Table[a[n], {n, 0, 37}]

%Y Cf. A000079, A000244, A006899, A372824, A372825, A372826.

%K nonn

%O 0,3

%A _Clark Kimberling_, May 18 2024