I had this case where I wanted to move articles from Blogger website to hosted Wordpress. As I can't make 301 redirects, I simply deleted the selected articles and scheduled to be published after 1 month. My question is does Google will really forget about those articles, so when they are published once again, they are indexed by the search engine? Should I make that period longer than 1 month?
I would not worry too much. Often people are concerned that Google will penalize them for stuff that they should be able to do. You are fine.
Google will figure things out okay. In fact, I am not not sure I would wait as much as a month, but if you want to be cautious, a month should be a good period of time. I would make sure, if you can, to deliver a 410 Gone error as opposed to a 404 Not Found error. This should clear out Google's index faster. Otherwise, Google will try to access your pages for a period until it finally drops your pages.
On the search site, there is no real memory effect. When your old pages are dropped from the index, Google does not keep old data in a data base.
What people do not realize is that there is a huge citation database that does somewhat remember things, not to penalize, but to follow citations and make appropriate linkage from page to page and site to site. In this respect, Google does remember things. But there is no overlap. The citation database is set up to give credit and not to penalize. Here Google will realize that your pages moved from one site to another and if there are any citations, or citations that you are not aware of, they will likely be adjusted.