A372824 Sequence formed as follows: for each k >= 0, insert between 3^k and 3^(k+1) the greatest power of 2 that is in the interval [3^k, 3^(k+1)], and then arrange the resulting numbers in nondecreasing order.
1, 2, 3, 8, 9, 16, 27, 64, 81, 128, 243, 512, 729, 2048, 2187, 4096, 6561, 16384, 19683, 32768, 59049, 131072, 177147, 524288, 531441, 1048576, 1594323, 4194304, 4782969, 8388608, 14348907, 33554432, 43046721, 67108864, 129140163, 268435456, 387420489
Offset: 0
Examples
3^0 <= 2^1 < 3^1 < 2^3 < 3^2 < 2^4 < 3^3 < ...
Crossrefs
Programs
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Mathematica
a[n_] := If[EvenQ[n], 3^(n/2), 2^Floor[((n + 1)/2) Log[3]/Log[2]]] Table[a[n], {n, 0, 37}] -
PARI
a(n) = if (n%2, 3^(n\2), 2^logint(3^(n/2), 2)); \\ Michel Marcus, May 23 2024