As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
AT LEVEL OFF AT FL350, COST INDEX 5, AS AUTO THROTTLES PULLED BACK TO CRUSE MACH WE FELT TWO QUICK THUDS IN SUCCESSION. F/A'S CALLED TO REPORT THE SAME NO UNUSUAL ENGINES INDICATIONS NOTED. JUMPSEATING PILOT THINKS ISSUE CAME FROM #1 SIDE. SUSPECTED POSSIBLE COMPRESSOR STALL. / R&R #1 ENGINE BLEED AIR CHECK VALVE PER AMM.