7Notes HD Premium does what you want (at least the text conversation, I have tested the searchability afterwards but I don't see why it wouldn't work). I think it's generally a good quality app, but I haven't had much luck with the handwriting to text conversion personally, probably because my hand writing is quite messy. It usually converts it wrong, so I spend too much time editing the conversation process. However, it might work better if your handwriting is a bit clearer than mine, I've seen others posting about the app having had better luck.