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Hi, I'm Mike and I'll be assisting you. Please stand by while I review your question.
The first thing I suggest is taking the blanket to another room and plugging it in to see if it still is blinking. This will show if the blanket or the outlet is the problem. Let me know the results.
The reason for checking it in a different outlet was to see if the control or the outlet was the problem. If it starts blinking again repeat the suggestion. You may have a bad connection in the outlet that causes the issue.