I did my Ph.D. 2 years ago. After that, I moved into the industry where I am now working in a similar field. I like to think that they would be happy to get a mail every now and then on what I have been up to or if I bump into some interesting research questions. I have been sending them a mail once every 8 months or so if I had something to share (e.g. a job opportunity, relevant research paper) or just for giving them an update on my professional life. It does not seem to annoy them.
But is it generally appreciated that I reach out/stay in contact? Or is it strange that I still contact them now and then?