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The items in the sequence should be numbered from 2 onwards, and then item $b$ is

the base-$b$ representation of $\lfloor b^2/4\rfloor$.

So the fraction that defines the sequence is

100/4.

The next few entries in the list would be:

30, 33, 37, 3B, 40, 44, 49, 4E, 50.

The items in the sequence should be numbered from 2 onwards, and then item $b$ is

the base-$b$ representation of $\displaystyle \left \lfloor \frac{b^2}{4} \right \rfloor$, which can also be written as just $\displaystyle \left \lfloor \frac{100}{4} \right \rfloor$, since $b$ in base $b$ is always $10$.

So the fraction that defines the sequence is

100/4

and the next few entries in the sequence are:

30, 33, 37, 3B, 40, 44, 49, 4E, 50.

The items in the sequence should be numbered from 2 onwards, and then item $b$ is

the first two digits of 1/4 in base $b$

(with leading zeros ignored in the first two cases). Equivalently, it's

the base-$b$ representation of $\lfloor b^2/4\rfloor$.

So the fraction is

1/4.

The next few entries in the list would be:

30, 33, 37, 3B, 40, 44, 49, 4E, 50.

The items in the sequence should be numbered from 2 onwards, and then item $b$ is

the base-$b$ representation of $\lfloor b^2/4\rfloor$.

So the fraction that defines the sequence is

100/4.

The next few entries in the list would be:

30, 33, 37, 3B, 40, 44, 49, 4E, 50.

The items in the sequence should be numbered from 2 onwards, and then item $b$ is

the first two digits of 1/4 in base $b$

(with leading zeros ignored in the first two cases). Equivalently, it's

the base-$b$ representation of $\lfloor b^2/4\rfloor$.

So the fraction is

1/4.

The items in the sequence should be numbered from 2 onwards, and then item $b$ is

the first two digits of 1/4 in base $b$

(with leading zeros ignored in the first two cases). Equivalently, it's

the base-$b$ representation of $\lfloor b^2/4\rfloor$.

So the fraction is

1/4.

The next few entries in the list would be:

30, 33, 37, 3B, 40, 44, 49, 4E, 50.