jmc

We first count the even terms of the sequence. Subtract $2$ from the list to get $4,$ $8,$ $12,$ $\dots ,$ $92,$ $96,$ and then divide by $4$ to get $1,$ $2,$ $3,$ $\dots ,$ $23,$ $24.$ So this list has $24$ numbers.

We then count the odd terms of the sequence. Subtract $3$ from the list to get $4,$ $8,$ $12,$ $\dots ,$ $92,$ then divide by $4$ to get $1,$ $2,$ $3,$ $\dots ,$ $23.$ So this list has $23$ numbers.

Now we sum up the above two numbers, which yield a total $24+23=\boxed{47}$ numbers.