B757 CREW REPORTS ACFT HAS SLIGHT NOSEWHEEL SHIMMY ON TAKEOFF; AFTER LANDING IT IS DISCOVERED THAT ONE NOSEWHEEL IS MISSING.

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PREFLT; TAXI OUT AND INITIAL TKOF ROLL WERE NORMAL. AT ABOUT 100 KTS WE FELT A SLIGHT SHIMMY FROM THE NOSEWHEEL. IT WAS NOT EXCESSIVE AND WAS SIMILAR TO OTHER SHIMMY PROBS I HAVE EXPERIENCED IN THE PAST ON THE B757. ACFT TRACKING AND PERFORMANCE APPEARED TO BE NORMAL AND IN MY JUDGEMENT IT WAS SAFER TO CONTINUE THE TKOF THAN TO RISK A HIGH SPD ABORT IN THE DARK. ZZZ; AT THE TIME; WAS IN NIGHT OPS. AT TOP OF CLB WE SENT AN ACARS MESSAGE TO MAINT REGARDING THE NOSEWHEEL SHIMMY. THE FLT CONTINUED AS NORMAL AND WAS UNEVENTFUL UNTIL WE ARRIVED AT ZZZ1. THE LNDG WAS NORMAL WITH NO HARD IMPACTS OR SIDE LOADS TO MAINS OR NOSEWHEEL. WHEN WE ENTERED RAMP WE WERE ADVISED BY AN OUTBOUND ACFT THAT WE WERE MISSING THE R NOSE LNDG GEAR (WHEEL). WE PARKED THE ACFT AND REQUESTED TUG-IN. UPON FURTHER INSPECTION BY MAINT IT WAS DETERMINED THAT THE ACFT SHOULD NOT BE REMOVED. WE KEPT THE FLT ATTENDANTS AND PAX INFORMED AND BUSES WERE DISPATCHED TO DISEMBARK PAX. AFTER THE PAX WERE SAFELY IN THE TERMINAL I WAS INFORMED THAT ACR SAFETY HAD CALLED ZZZ AND WAS NOTIFIED THAT A WHEEL WAS FOUND SOMEWHERE ON THE ARPT. LATER; I WAS ALSO INFORMED THAT A SWEEPER IN ZZZ HAD FOUND WHAT APPEARED TO BE BEARING PARTS ON THE RAMP AT AN UNDISCLOSED LOCATION. MY QUESTION IS WHY WERE WE NOT INFORMED OF THIS PRIOR TO LNDG? WE WERE ALOFT FOR OVER 3.5 HRS AND NOTHING WAS RELAYED TO THE FLT THAT EVEN HINTED THAT WE MIGHT HAVE A PROB. IT SEEMS TO ME THAT WITH AN ACARS NOSE LNDG GEAR MESSAGE SENT AND A WHEEL FOUND IN ZZZ; THAT SOMEONE IN MGMNT WOULD HAVE THE PRESENCE OF MIND TO PUT THE 2 EVENTS TOGETHER AND START INQUIRIES OR NOTICES TO ACFT THAT HAD DEPARTED ZZZ.