If you are trying to find the relative difference between the mean and the standard error then simply set up the inequality and solve for n.
If you are using a Wald test or a normal approximation then the standard error of the mean with a binomial is se = SQRT(p_hat*(1-p_hat)/n) where p_hat is the estimated value of the proportion which is just the mean of the sample data.
So you are looking at [1.96*se]/p_hat < t where t is your threshold (3% = 0.03) so extracting n we get:
(1.96)^2*(1-p_hat)/(p_hat*t^2) < n or
n > (1.96)^2*(1-p_hat)/(p_hat*t^2)
So you can find the first integer satisfying that condition and you have your sample size.
If you want to consider that p_hat can fluctuate within a specific range then you will need to do this for the lower and upper bounds and combine both information to get a value for n.