In my case, this error "Specified 'sqlite3' for database adapter, but the gem is not loaded. Add gem 'sqlite3' to your Gemfile." message showed up, when I ran rails server right after I generated a fresh rails app. It was with Rails version 4.1.16 (Ruby version 2.3.1)
gem 'sqlite3', '~> 1.3.0'
This line in Gemfile removed the error message. I think new sqlite gem (version 1.4) has a conflict with old rails (version 4.1) but I didn’t see any related issue on their Github repository. I’m adding this answer here because it might help anybody experiencing the same situation I’m in.