imc

We calculate more terms: $$1,3,4,7,11,18,\dots .$$ We find a pattern: if $n+2$ is a multiple of $3$, then the term is even, or else it is odd. There are $\lfloor \frac{2023}{3}\rfloor =\boxed{674}$ multiples of $3$ from $1$ to $2023$.