A Delta Air Lines crew reported receiving a Traffic Collision Avoidance System Resolution Advisory (TCAS RA) departing Washington-DCA on 28 March. ADS-B data received from the aircraft is also consistent with a TCAS RA. Delta flight 2983 was departing Washington for Minneapolis (MSP) when a flight of four US Air Force T-38s approached from the opposite direction at a reported barometric altitude of 800 feet (GPS altitude 875 feet). Both flights continued to their destination without incident, which was first reported by CNN.
This post has been updated to reflect additional information from the FAA that the T-38 flypast was a four-ship formation.

Delta 2983 departed Runway 19 at 19:16 UTC. At the same time DO61, the US Air Force T-38s were turning north on the east side of the Potomac River as they prepared to directly overfly the Pentagon and Arlington National Cemetery for planned funeral flypast. It is common for only one aircraft in a multi-ship formation to broadcast ADS-B data. The aircraft will remain in communication with air traffic control as “[CALL SIGN], flight of [NUMBER]”.

Shortly after transitioning from the DCA tower controller to the Potomac departure controller, Delta 2983 noted that they had received a TCAS RA and queried the controller if there had been an “actual aircraft” in the vicinity, according to audio capture by LiveATC.net. The controller answered in the affirmative.
The question from the Delta crew about an “actual aircraft” may be related to the recent phantom TCAS alerts experienced by multiple aircraft near DCA in recent weeks.
The Delta A319 continued to Minneapolis, arriving at 21:40 UTC. The T-38s returned to Langley Air Force Base in Virginia, landing around 19:51 UTC.
Flightradar24 data available for download.
Data available for download includes the CSV and KML files from the Delta A319 and the US Air Force T-38 that was broadcasting ADS-B.
Aircraft information
Delta Air Lines flight 2983 was operated by an Airbus A319-114 registered N342NB.
DO61, the T-38 broadcasting ADS-B, was operated by a US Air Force Northrop T-38A Talon registration 67-14833.
FAA Statement
Delta Air Lines Flight 2983 was cleared for takeoff at Ronald Reagan Washington National Airport around 3:15 p.m. local time on Friday, March 28, while four U.S. Air Force T-38 Talons were inbound to Arlington National Cemetery for a flyover.
The Delta aircraft received an onboard alert that another aircraft was nearby. Air traffic controllers issued corrective instructions to both aircraft. The FAA will investigate.