What was found
FILED ALTITUDE FL 410, WHILE DESCENDING FROM FL 410 TO JOIN LEGOZ 4 ARRIVAL. WE HAD LEVELED OFF AT FL 370 PRIOR WITH NO ISSUE, THEN FLAMEOUT AT FL 330. AT APPROXIMATELY 0900 ON 22 NOVEMBER, 2025 THE CREW EXPERIENCED A NR 1 ENGINE FLAMEOUT. IT OCCURRED AS WE LEVELED OFF AT 33,000 FT AND & WERE PUSHING THRUST LEVERS FWD TO MAINTAIN AIRSPEED. FIRST INDICATION OF AN ISSUE WAS THE NR 1 GEN OFF LIGHT & ASSOCIATED WARNING/CAUTION LIGHT. LT ENGINE OIL PRESSURE WARNING CAME ON PROMPTING US TO LOOK AT N1, N2 AND ITT GAUGES SHOWING 0 ITT & TURBINE SPIN DOWN. DECLARED AN EMERGENCY IMMEDIATELY DUE TO NEED TO GET TO OUR DRIFT DOWN ALTITUDE & LOOK FOR CLOSEST SUITABLE AIRFIELD TO LAND. ONCE ESTABLISHED ON A VECTORS & DESCENT PROFILE, PM BROKE OUT PCL TO A2 & RAN CHECKLIST. PF BEGAN SLOWING ACFT TO GET WITHIN THE 200 KIAS LIMIT FOR RESTART. ATTEMPTED RESTART ENGINE 1, UNSUCCESSFUL, ABORTED START. ENGINE RE-LIT ON IT'S OWN AND APPEARED TO BE FUNCTIONING NORMALLY; DID NOT INCREASE POWER IN A CONTINUOUS DESCENT. CONTINUED DESCENT , DESCENDING THOUGH ICING CONDITIONS AT 12,000 MSL WHICH TURNED ENGINES & WINGS ON FOR, UNTIL CLEAR. NR 1 ENG CONTINUED TO APPEAR NORMAL ALL THE WAY TO FINAL & MADE THE DECISION TO MAKE A TWO ENGINE APPROACH WITH PM READY TO ADJUST FLAPS IN THE EVENT THE ENGINE FAILED AGAIN. DUE TO THE STRONG GUSTING WINDS, DETERMINED A DUAL ENGINE APPROACH WOULD BE SAFEST IN THESE CONDITIONS, WITH THE PM CLOSELY MONITORING ENGINE FUNCTION TO TOUCHDOWN. LANDING WAS UNEVENTFUL AND WE TAXIED TO THE FBO WITHOUT FURTHER INCIDENT.