I usually use Google to connect to ESRI. However, I am beginning to work with the ArcGIS API for Python, and it needs an Arc password. How do I get to an Arc-specific password vice the social connection?
I haven't confirmed this yet, but I believe you need to use the Oauth2 workflow. This requires creating an Application item in ArcGIS online and obtaining a client ID and client secret. More detail in the doc below:
Working with different authentication schemes | ArcGIS for Developers