The way you're generating your addresses, using SHA256(string + n), better known to cryptographers as SHA256(string | n), is not secure. This is bad news if you're trying to generate these addresses but on the other hand it makes your task easier if your intention is to actually brute force them.

First of all, this is a simple brainwallet input where hackers simply have to guess the value of "string" and then append random junk for "n" to guess all the deriviations you'll ever do, thus getting all your private keys. There are several programs deployed right now by hackers that are cleaning out all brainwallets as we speak.

The second, less subtle vulnerability is that if you expose your "n" or whatever you use as the index, along with the algorithm used to turn the index into your random ascii "n", people don't have to know what your STRING is to caarry out a length-extension attack (search it on google) since you can look for proof of concepts for length-extension attack anywhere on Github and then adjust the PoC for your specific starting string.