A372826 -id:A372826 - cp's OEIS frontend

A372825 Exponents of 3 and 2 in sequence A372823.

0, 0, 1, 2, 2, 4, 3, 5, 4, 7, 5, 8, 6, 10, 7, 12, 8, 13, 9, 15, 10, 16, 11, 18, 12, 20, 13, 21, 14, 23, 15, 24, 16, 26, 17, 27, 18, 29, 19, 31, 20, 32, 21, 34, 22, 35, 23, 37, 24, 39, 25, 40, 26, 42, 27, 43, 28, 45, 29, 46, 30, 48, 31, 50, 32, 51, 33, 53, 34

Offset: 0

Clark Kimberling, May 18 2024

nonn

Cf. A372823, A372826.

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

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

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}]

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.

Original entry on oeis.org

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

Clark Kimberling, May 18 2024

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

Cf. A000079, A000244, A006899, A372823, A372825, A372826.

Interspersion of A000244 and A098232.

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

a(n) = if (n%2, 3^(n\2), 2^logint(3^(n/2), 2)); \\ Michel Marcus, May 23 2024

cp's OEIS Frontend

A372825 Exponents of 3 and 2 in sequence A372823.

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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.

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Maple

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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.

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