why app store keep asking me to update when i deleted the app

Mac App Store: Hiding and unhiding purchases

Do you have an external drive with a backup of your Mac HDD that may have a copy of the app on it?

the app is not showing in the purchased items

Did you purchase it? Does it show when you unhide hidden purchases? What happens if you try to update it?

An app is considered to be installed if it shows up in a Spotlight search of local volumes. Bring up a search window in the Finder by pressing the key combination command-F. Search This Mac for the name of the application. Delete all copies that are found.

You may have installed a hacked app, originally from the Mac App Store. It contains the receipt for a different app, downloaded using an account that you don't control. You need to identify and remove the hacked app.

Important: The app you need to remove is not necessarily the one named in the App Store alert. For example, if the App Store says you need to update "Twitter," the hacked app may be "Angry Birds" or something else entirely. Don't make any assumptions about which app you're looking for. To find it, you have to carry out a systematic search.

Triple-click anywhere in the line of text below on this page to select it:

kMDItemAppStoreHasReceipt=1

Copy the selected text to the Clipboard by pressing the key combination command-C.

In the Finder, press command-F to open a search window, or select

File ▹ Find

from the menu bar. In the search window, select

Search: This Mac

from the row of tokens below the toolbar. Below that is a popup menu initially showing Kind. From that menu, select Other...

A sheet will drop down. In that sheet, select Raw Query and click OK or press return.

Now there will be a text box to the right of popup menu. Click in that box and paste (command-V).

The search window will show all the App Store products you've installed. Compare those search results with the list of your purchases from the App Store. To see the complete list, you may need to unhide hidden purchases. If any apps were download from the App Store using other Apple ID accounts that you control, sign in to the store under each of those ID's and check the purchases.

At least one of the items listed in the search window is not among your purchases in the App Store. Move each such item to the Trash. You may be prompted for your administrator password. Empty the Trash.

Log out and log back in. Test.