This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372824 #16 Sep 01 2025 11:35:43
%S A372824 1,2,3,8,9,16,27,64,81,128,243,512,729,2048,2187,4096,6561,16384,
%T A372824 19683,32768,59049,131072,177147,524288,531441,1048576,1594323,
%U A372824 4194304,4782969,8388608,14348907,33554432,43046721,67108864,129140163,268435456,387420489
%N 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.
%e A372824 3^0 <= 2^1 < 3^1 < 2^3 < 3^2 < 2^4 < 3^3 < ...
%t A372824 a[n_] := If[EvenQ[n], 3^(n/2), 2^Floor[((n + 1)/2) Log[3]/Log[2]]]
%t A372824 Table[a[n], {n, 0, 37}]
%o A372824 (PARI) a(n) = if (n%2, 3^(n\2), 2^logint(3^(n/2), 2)); \\ _Michel Marcus_, May 23 2024
%Y A372824 Cf. A000079, A000244, A006899, A372823, A372825, A372826.
%Y A372824 Interspersion of A000244 and A098232.
%K A372824 nonn,changed
%O A372824 0,2
%A A372824 _Clark Kimberling_, May 18 2024