I'm getting those calls, too, usually with no message, and one time I picked up and didn't say anything, but the line was quiet. One time I did get a recorded message from ConEdison, my electric provider, that I believe came from that number, asking if my power had been restored. (I had a power outage for several days due to the recent snow.) I can't be 100 percent sure it was ConEd since I wasn't home when the message was left, but the recorded message time seemed to match the Caller ID time from the 347-334-4378 number.
Did any of you recently have a power outage that you reported to your electric provider? If so, it might by their automated system calling back to see if your power is back up and on line.