A372824 -id:A372824 - cp's OEIS frontend

A372826 Exponents of 3 and 2 in sequence A372824.

0, 1, 1, 3, 2, 4, 3, 6, 4, 7, 5, 9, 6, 11, 7, 12, 8, 14, 9, 15, 10, 17, 11, 19, 12, 20, 13, 22, 14, 23, 15, 25, 16, 26, 17, 28, 18, 30, 19, 31, 20, 33, 21, 34, 22, 36, 23, 38, 24, 39, 25, 41, 26, 42, 27, 44, 28, 45, 29, 47, 30, 49, 31, 50, 32, 52, 33, 53, 34

Offset: 0

Clark Kimberling, May 18 2024

Cf. A372824, A372825.

a[n_] := If[EvenQ[n], n/2, Floor[((n + 1)/2) Log[3]/Log[2]]]
Table[a[n], {n, 0, 120}]

a(2n) = n, a(2n+1) = greatest k such that 2^k < 3^(n+1).

A372823 Sequence formed as follows: for each k >= 0, insert between 3^k and 3^(k+1) the least power of 2 that is in the interval [3^k, 3^(k+1)], and then arrange the resulting numbers in nondecreasing order.

Original entry on oeis.org

1, 1, 3, 4, 9, 16, 27, 32, 81, 128, 243, 256, 729, 1024, 2187, 4096, 6561, 8192, 19683, 32768, 59049, 65536, 177147, 262144, 531441, 1048576, 1594323, 2097152, 4782969, 8388608, 14348907, 16777216, 43046721, 67108864, 129140163, 134217728, 387420489

Offset: 0

Clark Kimberling, May 18 2024

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

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

[seq(op([3^i, 2^ceil(log[2](3^i))]),i=0..50)]; # Robert Israel, May 22 2024

a[n_] := If[EvenQ[n], 3^(n/2), 2^Ceiling[((n - 1)/2) Log[3]/Log[2]]]
Table[a[n], {n, 0, 37}]

cp's OEIS Frontend

A372826 Exponents of 3 and 2 in sequence A372824.

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