For all friends of SharePoint Server on Premises: Microsoft has published on 7th of March 2017 an Update for the old Sync Client called “Groove.exe”. The last Update was released at December 2016

No, I do not have good news. The Next Generation Sync Client is still syncing only to Office 365

KB3178645 Office 2013 KB3141458 Office 2016

Changes the priority ranking of certain error messages that are shown to users to adjust actionability and severeness. OneDrive for Business may crash during the synchronization process. OneDrive for Business may be stuck in a permanent error state while you try to synchronize a library.

Both Updates are valid only for MSI Installations, not Click to run.

before 3/7/2017	after 3/7/2017

Be aware that the update in Download Center applies to Microsoft Installer (.msi)-based edition of Office 2013. It doesn’t apply to the Office 2013 Click-to-Run editions such as Microsoft Office 365 Home

To determine whether your Office installation is Click-to-Run or MSI-based, follow these steps:

1. Open an Office 2013 application, such as Microsoft Word 2013.
2. On the File menu, select Account.
3. For Office 2013 Click-to-Run installations, an Update Options item is displayed. For MSI-based installations, the Update Options item isn’t displayed.

You will found the file groove.exe here:  X:\Program Files\Microsoft Office\Office15 for Office 2013 and  X:\Program Files\Microsoft Office\Office16 for Office 2016

So the version for Office 2013 of the file should be 15.0.4907.1000 or higher.
And the version for Office 2016 of the file should be 16.0.4504.1000 or higher.