First, install Ruby 2.2 or newer.  The Ruby installation should come with
Rubygems (the package-manager for Ruby stuff) preinstalled.  Using Rubygems,
you can install Twittbot with `gem install twittbot`.  After doing that the
`twittbot` command should be available in your system.

You would create a new bot using `twittbot new my-bot` from the terminal, then
cd’ing in that directory and authenticating using `twittbot auth`.
Then you create a new .yml file in the ./etc directory which contains all the
IDs I want to tweet at that looks like this:

nilsding@localhost:~/tmp/my-bot> cat etc/announcement.yml
---
:ids:
- 1234
- 4567
- 8901
:already_tweeted: []

Now comes the actual code.  For that, create the file
lib/announcement.rb which looks like this:

Twittbot::BotPart.new :announcement do
  every 30, :minutes do
    ids = @config[:ids].shift(15)  # take 25 ids at a time
    next if ids.empty?  # do not do anything if there are no ids anymore

    ids.each do |id|
      begin
        # look up the user name behind the ID, keep in mind that the
        # endpoint for that might be rate limited
        username = bot.user(id, skip_status: true)&.screen_name
        if username.nil?
          @config[:ids] << id
          next
        end

        # finally, tweet the message:
        bot.tweet "@#{username} Hey, check out my cool site!”
        # and add the id to the :already_tweeted list
        @config[:already_tweeted] << id
      rescue => e
        puts "fatal error: " + e.message
        @config[:ids] << id
      end
    end

    bot.save_config
  end
end

This is untested Ruby code, but should do what I want.

You can run this bot using the `twittbot start` command.  If everything works
it should start tweeting at the first 25 ids right away